Class Note – Dr Dr Chinmoy Jana, IISWBM, Kolkata Statistics – In plural sense- A set of numerical figures usually obtained by measurement or counting. In singular sense – subject of scientific activity which deals with the theories & methods of collection, analysis & interpretation of such data. Characteristics: (i) All available information are expressed in quantitative terms (ii) Its must be aggregates of facts. (iii) It is related to some field of inquiry stray collection of figures will be of n o use. (iv) It should be capable of being related to each other so that cause and effect relationship can be established. (v) It is affected by a multiplicity of causes. (vi) Exactness can not be guaranteed. Limitation : (i) It can be applicable only to quantitative data. (ii) It can be used to analyze only collective methods, not individual events. (iii) Statistical decisions are applicable only on the average & in long run. (iv) Statistical method should be handled with utmost care and experts only. (v) Data must be uniform – uniform – i.e. i.e. subject to a stable causal system. Primary data : Collected for a specific purpose directly from the field of arguing & so original in nature. Secondary data: Previously collected for one purpose & merely completed from that source for one is a different connection. i.e. collected by one and used by another, or collected for one purpose and used for another. Rounding of numbers : Number 54.38 rounded to the nearest unit 54 because digit 3 sent to the unit place is less than 5, when rounded to one decimal, it is 54.4, because digit 8 unit to first decimal place is more than 5. Difficulties arise when the digit to be dropped is exactly 5. Rule (a) When 5 is followed by b y digits all of which are not zero, then preceding digit is increased by one. 72.5002 ~ 73, 12.7537 ~ 12.8 (b) When 5 is last digit or is followed by b y zeros, it has become conventional to round the preceding digit to a even number. 72.5 ~ 73, 12.85 ~ 12.8, 41500 ~ 42 thousand, 3.245 ~ 3.24, 3.255 ~ 3.26 Absolute, Relative & Percentage Errors: Take a conception on the numbers like 5.2 means a number between 5.2 ± 0.5, 5.20 means a number between 5.20 ± .005. Unless otherwise stated, an observation of a continuous variate should be interpreted as extending half a unit of the last place below to half a unit above the rounded value. Absolute error of a measurement is its difference from the true value. Relative error is the ratio of absolute error to the true value. It is usually expressed as a percentage & the n called percentage error. Absolute error : Difference between measurement & true value. Relative error : Absolute error / True value Percentage error : Relative error × 100.
Problem: True value of up to 5 decimal is 3.14159. Find absolute error, relative error and percentage error, if is approximate by 22/7 Significant figures: Starting from the first non zero digit on the left to the end of the last digit accurately specified in the right. Number Significant 604 ~3 7.0 ~2 0.80 ~2 18.00 ~4 0.003 ~1 0.0030 ~2 3.20 ~3 Q. Rounding off the numbers upto two decimal points 12.345 15.365 18.355 38.445 87.454 5.55 12.555 17.3353 29.965 87.444 Q. Write the significance numbers of the following 0.082 8.082 0.002 8.882 5.090 0.007 3.202 0.0200 1.1120 0.05010 Observation, frequency : The data obtained are known as observations. Frequency of a value of the variable is the number of times its occurs is a given series of observations. Simple series : A series of observation recorded without any definite systematic arrangement. Frequency distribution : A statistical table which shows the variable arranged in ord er of magnitude, either individually or in group, & also the corresponding frequencies side by side. Simple frequencies Distribution shows the value of the variable individually grouped frequency distribution shows the value of the variable groups or individuals. Median – Median of a set of observations is the value of the middle-most item when they are arranged in order of magnitude. It can be calculate from a grouped frequency distribution either (i) by using simple interpolation in a cumulative frequency distribution, or (ii) by using the formula N 2 F Median = l 1 c fm
l 1 lower boundary of median class. N = Total frequency F = Cumulative frequency f m = frequency of median class. c = width of median class. Mode: Mode of a set of observations is that value which occurs with the maximum frequency. It is the most typical or fashionable value and at times represents the true characteristic of the frequency distribution as a measure of central tendency. In the case of a simple frequency distribution, mode can be found by inspection only. However, in the case of a grouped frequency distribution, it is difficult to find the mode accurately. It is generally calculated by the formula: where ,
Mode l 1
d 1 d 1 d 2
c
where l 1 lower boundary of the modal class; d 1 difference of frequencies in the modal class and the preceding class; d 2 difference of frequencies in the modal class and the following class; c common width of classes. The formula is applicable only when all classes have the same width. Mode has certain peculiarities too. When all observations occur with equal frequency, mode dose not exist. Again, there is more than one mode, if two or more values occur with the maximum frequency. Measure of dispersion: The ward dispersion is used to denote the „degree of heterogeneity‟ in the data. It is an important characteristic indicating the extant to which observations vary among themselves. The dispersion of a given set of observations will be zero, only when all of them are equal. The wider the discrepancy from one observation t o another, the larger will be the dispersion. Standard Deviation : Standard Deviation of a set of observations is the square root of the arithmetic mean of squares of deviations from arithmetic mean. In short, SD may be defined as “R oot-Mean-SquireDeviation from mean”. It is usually denoted by the Greek small letter (sigma). If
x1 , x2 ,......... ....., xn be a set of observations and x their A.M. then,
Square Deviation from mean : x
x , x
Deviation from mean : x1 x , x2 x .......... ........ xn x 2
1
x ................, xn x 2
2
2
Mean-Square Deviation from mean: 2 2 1 x1 x x 2 x ......... x n x n Root-Mean Square-Deviation from mean, i.e.
Standard Deviation
1
x n
1 x 2
n
i
x
2
x
2
i
2
The square standard deviation, i.e. 2 , is known as Variance. Variance = (S.D) 2 1 For simple series 2 xi x n 2 1 For frequency distribution, 2 f i xi x N Illustration I. A.M. of 8, 1, 6 is 1 1 x (8 1 6) 15 5 3 3 Illustration II. A.M. of 8, 1, 6 with frequencies (or weights) 3, 2 , 5 respectively is (here N =3+2+5 = 10) 1 x 3 8 2 1 5 6 56 10 5.6 10 Q: The arithmetic mean of two observations is 25 and there geometric mean is 15. Find (i) there harmonic mean and (ii) the two observations
Q: Find the median and median class of the data given below:Class boundaries 15-25 25-35 35-45 45-55 55-65
Frequency
4
11
19
14
0
65-75 2
Q: It is known that in the following incomplete frequency distribution, the total frequency is 1000 and that the median is 413.11. Estimate by calculation the missing frequencies. Values 300-325 325-350 350-375 375-400 400-425 425-450 450-475 475-500 Frequency 5 17 80 ? 326 ? 88 9 Q: It is known that in the following incomplete frequency distribution, the total frequency is 150 and that the median is 146.25. Estimate by calculation the missing frequencies. Values 100110- 120130- 140- 150- 160- 170- 180- 190110 120 130 140 150 160 170 180 190 200 Frequency 4 7 15 ? 40 ? 16 10 6 3 Q: Find the modal wages from the following table. Wages Rs. 50.0060.0070.0059.99 69.99 79.99 No. of employee 8 10 16
80.0089.99 14
90.0099.99 10
100.00109.99 5
110.00119.99 2
Q: A person bought 6 rupees worth of orange from five markets at 15p, 20p, 25p, 30p and 50p per orange respectively. What is the average price of an orange? What would be the average price, if he had purchased 20 oranges from each market? Q: The mean and S.D. calculation from 20 observations are 15 and 10 respectively. If an additional observation 5, left out through oversight, be included in the calculations, find the corrected mean and S.D. Q. The frequency distribution of monthly income (in Rs) of 200 families in a community is as under in which frequencies for two classes are missing: Income 3-5 5-7 7-9 9-11 11-13 Total (Rs „000) Number of 32 ? 57 ? 25 200 families The average monthly income is known to be Rs 7740. Find the missing frequencies.
Q. The mean and s.d. of heights of male students in a class are 162 cm and 10cm respectively; and the mean and s.d. of heights of 40 female students in the class are 150.75 cm and 8 cm respectively. Find the mean and s.d. for the entire class. Q. The distribution of Intelligence Quotient scores measured for 100 students in a test is as follows: IQ 40-50 50-60 60-70 70-80 80-90 90-100 Number of students 10 20 20 15 15 20 Find the Arithmetic Mean and Median.
The S.D. calculated from a set f 32 observation is 5. If the sum of the observations is 80, Q what is the sum of the squares of these observations? Q. The mean income per month of a friendly society of 25 members is Rs 350 and the S.D. is Rs 50. Five more members are admitted to the society and their incomes in Rs per month are 260, 300, 320, 490 and 590. Find the mean and S.D. of income for the new group of 30 members. Q. In a batch of 10 children the IQ of a dull boy is 36 below the average IQ of the other children. Show that the S.D. of IQ for all children can not be less than 10.8, If this S.D. is actually 11.4 determine what the S.D. will be when the dull boy is left out. Q. If the average weekly income of workers in a factory is Rs 520 and average weekly income f male and female workers are Rs 540 and Rs 460 respectively, then determine the ratio of male and female workers in the factory. What will be the number of female workers if the number of male workers is 330? Q. Arithmetic Mean of following frequency distribution f marks for a group of 60 students is 30.5. Calculate the missing value Marks 10 20 ? 40 50 Students 8 10 20 15 7 Q. For the following table, the mean is 1.46, calculate the missing frequency Student 0 1 2 3 4 5 Frequency 46 ? ? 25 10 5 Q. Calculate Mean. Class Interval 20-29 30-39 40-49 50-59 60-69 70-79-80-89 Frequency 02 04 08 27 18 15 06 Q. Following table shows monthly wage distribution of 130 workers in a factory, obtain Mode of distribution. Monthly Wage (in Rs) 1500-1700 1700-1900 1900-2100 2100-2300 2300-2500 Workers 25 30 37 27 11 Q. Frequency distribution of the number of students absent in a statistics class for a month is given below. Find the Median Number of students Absent 0 1 2 3 4 5 Days 2 1 4 10 3 2 Q. Obtain Median for the following frequency distribution of house rent for a sample of 30 families in a locality. Rent(Rs) 1800-2000 2000-2200 2200-2400 2400-2700 2700-3000 3000-3500 Number 04 07 10 05 02 02 of Families
Correlation & Regression Covariance : 1 ( x x)( y y) Cov( x, y) n
xy x y n n
n
Correlation Coefficient: cov( x, y ) r
n
y
( x x)( y y) ( x x) ( y y) n xy x y n x x n y y 2
2
2
2
2
2
Q: Calculate the correlation coefficient from the following results. 100
x i 1
i
100
100
i 1
i 1
100
100
280, yi 60, xi 2384, yi 117, xi y i 438 2
i 1
2
i 1
Q: Find the coefficient of correlation from the following data.
X 65 63 67 64 68 62 70 Y 68 66 68 65 69 66 68 Q: Calculate the coefficient of correlation from the following data. x y
66 65
2.52 2.49 2.49 2.45 2.43 2.42 2.41 2.40 730 710 770 890 970 1020 970 1040
Q: The following table gives the index numbers of industrial production in a country and the number of registered unemployed persons in the same country during the eight consecutive years. Calculate the coefficient of correlation and comment on the result. Year 2004 2005 2006 2007 2008 2009 2010 2011 Index of Industrial 100 102 103 105 106 104 103 98 production No of registered 10.5 11.4 13.0 11.5 12.0 12.5 15.6 20.8 unemployed (in thousands)
Q: Marks obtained by 10 students of PSM in Mathematics and economics are given below: Mathematics (X) 32 38 48 43 40 22 41 69 35 64 Economics (Y) 30 31 38 43 33 11 27 76 40 59 Calculate the correlation coefficient
Q. Calculate the correlation coefficient from the following data of sales and net-profit for some top Auto-makers during the quarter July-September 2011. Company Fata Bhero Jahaj GAD Bharat Ashoke MM&MM Babaruti Motor Anda Auto Motor Horse Lele Udyog Average 7836 8051 24 10 5 16 24 34 Sales (Rs in Hundred Crore) Average 47 22 34.5 3.5 6 9 20 32 Net Profit (Rs in Ten Crore)
Regression: The word regression is used to denote estimation or prediction of the average value of one variable for a specified value of the other variable. Regression equation of y on x is y y b yx ( x x).
x x b xy ( y y)
Regression equation of x on y is Where
b yx
Regression coefficient of y on x is
b yx
Regression coefficient of y on x is
y y
x x r
And
x x
y
x 24 x 164
x on y
r
y
x
cov( x, y ) 2 x
r
y
x
x
Q: Find the regression of
2 x
y y r
x
cov( x, y )
y
from the following data.
y 44 xy 306 y 574 n 4
2
2
Then find x when y = 6. Q: The following data show the maximum and the minimum temperatures (degree centigrade) on a certain day at ten important centers located throughout India: Max. temp. (x)
29
23
25
15
27
29
24
31
22
28
Min. temp. (y)
8
3
7
5
8
19
10
7
5
11
x
2
It is known that for the given data line of
y
on x .
6595, y 2 867, xy 2193. Find the regression
Q: From the following results, obtain the two regression equations and estimate the yield of crops when the rainfall is 22 cms, and the rainfall when the yield is 600 kg. : y
Mean S. D
(Yield in kg)
x ( Rainfall in cm. )
508.4 36.8
26.7 4.6
Q: The following results were obtained from records of age ( x) and systolic blood pressure ( y ) of a group of 10 women Mean Variance
x
y
53 130
142 165
( x x)( y y) 1220 Find the appropriate regression equation and use it to estimate the blood pressure of a woman whose age is 45. Q: Find the equation of the line of regression of x on y for the following data: x 1.0 1.5 2.0 2.5 3.0 3.5 4.0 y 5.3 5.7 6.3 7.2 8.2 8.7 8.4 Q. Marks obtained by 12 students in the Mid semester (x) and Final semester (y) are as follows: x 41 45 50 68 47 77 90 100 80 100 40 43 y 60 63 60 48 85 56 53 91 74 98 65 43 What is your estimate of the marks you could have obtained in the final semester if you obtained 60 in the mid semester. Q. Let the lines of regression concerning two variables x and y given be y=32-x and x=13-0.25y. Obtain the values of the means and then correlation coefficient.
Time series: Q: In a study of it‟s sales, a motor company obtained the following least squares trend equation y 1600 200 x [ origin 2000, x unites 1 year, y = total no of unites sold annually] The company has physical facilities to produce only 3600 unites a year and it believes that at least for the next decade the trend will continue as before. (a) What is the average annual increase in the number of units sold? (b) By what year the companies expected sales have equaled its present physical capacity? (c) Estimate the annual sales for 2015. How mach in excess of the companies present physical capacity in this estimate value?
Q: Fit a straight line trend by the least square method to the following figures of production of a sugar factory. Year (y) production `000 tons
1999 76
2000 87
2001 95
2002 81
2003 91
2004 96
2005 90
Estimate the production of 2006 Q: Fit a straight line trend equation by the method of least square from the following data & then estimate the trend value for the year 1915. Year
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Value
65
80
84
75
77
71
76
74
70
68
Q. Fit a straight line trend by the method of least squares to the following data on population of a state and find the trend value for January 2012 Year 2006 2007 2008 2009 2010 2011 Population 21 22 27 32 34 35 (in lacs)
Index Number Q: Find Index Number by the (a) method of aggregates, and (b) method of relatives ( using arithmetic mean), from the following: Commodity Rice Wheat Pulse Fish
Base Price 35 30 40 107
Current Price 42 35 38 120
Q: Construct Fisher‟s ideal index number for the data: Commodity
2000 ( Base year) Price Quantity 8 6 10 5 7 8
A B C
2008 (Current year) Price Quantity 12 5 11 6 8 5
Q: Calculate the price index numbers from the following data, using (i) weighted aggregative formula, and (ii) weighted arithmetic mean of price relative formula : Commodity
Unit
A B C D E
Quintal Kg. Dozen Litre Lb.
Price (Rs.) per unit Base period Current period 80 110 10 15 40 56 50 95 12 18
Weight 14 20 35 15 16
Q: From the following price & quantity data, compute . Laspeyer;s and Paascher‟s Price Index number for 2010 with 2000 as base. Commo dity A B C
p o
Price
2000 4 60 35
p n
(Rs./kg.)
2010 5 70 40
Sold
qo
qn
Quantities 95 118 50
(kg.) 120 130 70
Q. Calculate the following price index number for the year 2012 with 2002 as a base year. i. Simple aggregative price index ii. Weighted aggregative price index iii. Laspeyer;s Price Index iv. Paascher‟s Price Index v. Fisher‟s price index Commodity
Unit
A B C
Kg Kg mt
2002 ( Base year) Price Quantity 20 50 15 100 5 150
2012 (Current year) Price Quantity 30 60 45 120 10 100
Q. Price relatives in percentage and weights of a set of commodities are given below Commodity Price Relative in Weights Price X Weight Percentage X 115 W1 115 W1 Y 110 W2 110 W2 Z 125 2W1 250 W1 T 116 W2 - 2 116W2 -232 If the sum of weights is 30 and the price index no. is 118% Find the value of W1 and W2 Q. Determine the all types f price index number using the following data Commodity
Unit
Weight
A B C D
Kg Mt Mt Lit
30 15 5 12
2002 ( Base year) Price Quantity 30 100 10 110 80 70 25 200
2012 (Current year) Price Quantity 35 120 16 90 100 80 45 250
Q. Find the price Index number using weighted arithmetic mean of price relatives for the following data Commodity
A B C D
Unit
Kg Dozen Qt Lit
Weight
14 20 35 15
Base year 90 10 40 50
Price Current Year 120 17 60 95
Probability
Q. 1What is probability? Define experiment, random experiment, event, elementary event, composite event. Q. 2 Define with examples mutually exclusive, equally likely and exhaustive events Q. 3 What are the differences between Laspeyr‟s index number and Pasche‟s index number. Q. 4 Write the formula‟s of Bowel‟s index number and Fisher‟s Ideal index n umber. Q. 5 Two coins are tossed what is the probability of getting a. both heads [Ans. ¼] b. at least one head [ 3/4] c. one head and one tail [1/2] Q. 6 One Die is thrown, what is the probability of getting d. an even numbered face [1/2] e. less than 3 numbered face [1/3] Q. 7 Two dies are thrown and points are multiplied, what is the probability that product is 12? [1/9] / / / Q. 8 Given P(A)= ½, P(B)= 1/3 and P(AB)=1/4, Find P(A+B), P(A/B), P(A +B) and P(A B ). Q.9 A bag contains 6 white and 4 black balls, one ball is drawn, what is the probability that it is white. [3/5] Q. 10 Two balls are drawn from a bag containing 3 white and 5 black balls, what is the probability f. First one is white and second one is black [15/56] g. One is white and other is black [30/56] h. Both are black [20/56] Q. 11 Two cards are drawn from a full pack, what is the probability that i. both are red [25/102] j. one is heart and other is diamond [13/102] Q. 12 What is the probability that 3 children of a family having different birthday. [0.992] Q.13 Five students seat in a row at random, what is the probability that Payel and Gargi sit next to each other. [2/5] Q. 14 Five coins are tossed simultaneously, find the probability that at least one head turns up. [31/32] Q. 15 If the letters of the word “RAMESH” be arranged at random, what is the probability that there are exactly 3 letters between A and E? Q.16 A card is drawn at random from a well shuffled pack. What is the probability that it is a spade or king? Q. 17 Two unbiased dice are thrown. Find the probability of getting k. An odd sum l. 3 at least on one die. Q. 18 Shyamal and Bimal stand in a line with 10 other students. What is the probability that there are 3 students between Shyamal and Bimal. Q.19 An integer is chosen at random from 100 integers 1, 2, 3, … , 100. What is the probability that the selected integer is divisible by 11 or 15? Q. 20 What is the probability that a leap year, selected at random will contain 53 Mondays?
Q.21 If A and B are independent events and P(A) = 3/5, P(B)=2/3,find P(AB) and P(AB). Q. A bag contains 7 red and 6 black balls. Two balls are drawn without replacement. What is the probability that the second ball is red if it is known that the first is red? Q. Two dice are thrown getting two numbers whose sum is divisible by 4 or 5 is considered a success. Find the probability of success. Q. Find the probability that an ordinary year, selected at random will contain 53 Wednesdays. Q. 4 shirts are defective out of 10 Shirts in Rajib‟s retail shop, 3 shirts are purchased, what is the probability that no one is defective. [1/6] Q. 10 distinguishable balls are poured in 4 boxes. What is the probability that a specified box 8 10 contain exactly 2 balls. [(48*3 )/4 ] Q. 4 cards are drawn at random from a full pack, what is the probability that they are from a. different suits. [2197/20825] b. Different suits and denominations [264/4165] c. Same suit [44/4165] Q. A card is drawn from each of two well-shuffled packs of cards. Find the probability that at least one of them is ace. [25/169] Q. A machine consists 2 parts, A and B. Gourav sells part A in which 9 out of 100 are likely to be defective. Sanjoy sells part B in which 5 out of 100 are likely to be defective. What is the probability that an assembled machine is not defective. [0.8645] Q. Bag A contains 2 white and 2 black balls and bag B contains 2 white and 4 black balls. a. Draw one from each, what is the probability both are same colour. [1/2] b. If a bag is selected at random and one ball is drawn from it, what is the probability that it will be white? [5/12] Q. A bag contains 8 white and 6 blackballs, 5 balls are drawn, what is the probability that 3 white and 2 black balls are drawn. [60/143] Q. There is 50-50 chance that Jinat will appear an interview. The probability that Sharmila will get the job is ¾ if Jinat does not appear the interview and it is 1/3 if Jinat appears the interview. What is the probability that Sharmila will get the job? [13/24] Q. Three coins are tossed what is the probability of getting a. 0 head, 1 head, 2 heads, 3 heads [1/8, 3/8, 3/8 1/8] b. more than one head [1/2] c. at least one head [7/8] Q. There is 80 % chance to convince in any matter to Dr. X. Nilanjana and Jethly tried independently, what is the probability that at least one of them can convince Dr. X. [24/25] Q. A coin is tossed 10 times. Find the probability of getting (i) exactly 6 heads and (ii) 9 heads and 1 tail. Q. Two players Kankana and Ranjana are throwing a die alternately, she who first throws a six wins the game. Kankana begins, what is the probability that 1. Kankana wins. [6/11] 2. Ranjana wins [5/11] 3. st Q. The overall % of failure in Retail 1 sem exam is 40. What is the probability that out of a group of 6 candidates at least 4 passed the exam? [1701/3125]
Q. X is discrete random variable having probability mass function X 0 1 2 3 4 5 6 7 P|X=x 0 K 2k 2k 3k K 2k 7k +k Determine the constant k. Find P(X<6) and P(X6). [1/10, 0.81, 0.19] st Q. Probability that a student of 1 sem in Retail course having PG degree is0.4. Determine the probability that out of 5 students none, one and at least one have PG degree. [0.92224] Q. Five coins are tossed 6400 times. Find the expected frequencies of the distribution of heads and tails. Q. In 10 independent throws of a defective die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. Find the probability that an even number will not appear at all in10 independent throw of the die. 10 [(3/8) ] st Q. In Retail 1 sem exam 25% of the students failed in math, 15 % failed in economics and 10 % failed in both math ad eco. A student is selected at random a. If he failed in economics, what is the probability that he failed in math [2/3] b. If he failed in math, what is the probability that he failed in economics [2/5] c. What is the probability that he failed in both the eco and math. [3/10] Q. A random Variable x follows Poisson distribution with parameter 3, Find the probability that the variable assumes the values a. 0, 1, 2, 3 [0.0498, 0.1494, 0.2241, 0.2241] b. less than 3 c. at least 2 -3 given that e = 0.0498 Q. Rajib receives on an average 2.5 telephone calls per day during 10:00 am to 10:10 am. Find the probability that on the da y of math exam during the same time period Rajiv receives a. no call. [0.0821] b. Exactly 4 calls [0.1336] -2.5 Given that e =0.0821 Q. In manufacturing process of toys in a factory on an average 10 % becomes defective. Madhumita chosen 10 toys at random, what is the probability that exactly 3 are defectives. Use Poisson approximation to the Binomial distribution. [0.061, 0.057] Q. Two defective tube lights are mixed with 8 non-defective tube lights. A sample of 3 tubes is taken at random from the lot and tested for number of defectives. Find the probability distribution of the number of defective tube lights in the sample and tabulate the probabilities. Q. Ajay can hit a target 3 times in 4 shots, Debasis 4 times in 5 shots and Susanta once in 3 shots. They fir together, what is the probability that a. The target is destroyed [29/30] b. Two of them hit the target [31/60] c. All the three are successful [1/5] 0 Q. Suppose the temperature during October is normally distributed with mean 68 F and 0 0 0 standard deviation 6 F. Find the probability that the temperature is between 62 and 80 F. [0.82]
Q. The probability that an Indian bomb dropped from an aircraft will strike the target is 1/5. If six bombs are dropped, find the probability that i) Exactly two will strike the target [0.246] ii) At least two will strike the target [0.345] Q. Su ppose 2 % of the items made by Jayanta‟s co is defective. Find the probability that -2 there are 3 defective items in a sample of 100 items. given e =0.135. [0.180] Q. A picnic is to be organized on a particular day. The weather forecast says that there is 50 % chance of raining on that day. If it rains, the probability that the picnic is good is 0.30 and if it does not then the probability is 0.90. What is the chance that the picnic will be good on that day? Q. A man draws 2 balls from a bag containing 4 white and 6 black balls. If he is to receive Rs 9.00 for every white ball which he draws and Rs 6.00 for every black ball, What is his expected gain? Q. The number of burglaries in a city has an average of 6 per month (assuming 30 days in a -0.2 month). What is the probability that there will be 3 or more burglaries in a day? Given e = 0.8187. Q. The probability that a given line of computer code has a mistake in it is 0.02. Suppose that there are 20 such lines of code and the mistakes occur independently from line to line. Find the probability of (i) no mistake, (ii) two or more mistakes.
