STATISTICS & PROBABILITY DECEMBER 5, 2017 (TUESDAY) following: Individual Activity: Answer the following: 1.
How many different samples of size n=3 can be selected from a population with the following sizes? a. N = 4 b. N = 8 c. N = 20 d. N = 50
2.
Samples of three cards are drawn dr awn at random from a population of eight cards numbered from 1 to 8. a. How many possible samples can be drawn? b. Construct the sampling distribution of sample means. c. Construct a histogram of the sampling distribution of the means.
3.
A population has a mean of 60 and a standard deviation of 5. A random sample of 16 measurements is drawn from this population. Describe the sampling distribution of the sample means by computing its mean and standard deviation. Assume that the population is infinite.
4.
The heights of male college students are normally distributed with mean of 68 inches and standard deviation of 3 inches. If 80 samples consisting of 25 students each are drawn from the population, what would be the expected mean and standard deviation of the resulting sampling distribution of the means? Assume that the population is infinite.
5.
Find the finite population correction factor given the following: a. N = 200, n = 10 b. N = 2 000, n = 10 c. N = 400, n = 40 d. N = 500, n = 10 e. N = 200, n = 20
6.
Consider all samples of size 5 from this population: 2 5 6 8 10 12 13 a. Compute the mean and standard deviation of the population. b. Calculate the mean of the sampling distribution of the sample means. c. Calculate the standard deviation of the sampling distribution of the sample means.
7.
The scores of individual students on a national test have a normal distribution with mean 18.6 and standard deviation 5.9. At Federico Ramos Rural high School, 76 students took the test. If the scores at this school have the same distribution as national scores, what are the mean and standard deviation of the sample mean for 76 students? Assume that the population is infinite.
8.
A manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 120 hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is less than 900 hours?
9.
The average cholesterol content of a certain canned goods is 215 milligrams, and the standard deviation is 15 milligrams. Assume that the variable is normally distributed. a. If a canned good is selected, what is the probability that the cholesterol content will be greater than 220 milligrams? b. If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be larger than 220 milligrams?
10. The average public high school has 468 students with a standard deviation of 87. a. If a public school is selected, what is the probability that the number of students enrolled is greater than 400? b. If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is between 445 and 485?
STATISTICS & PROBABILITY DECEMBER 7, 2017 (THURSDAY) Individual Activity: Solve the following problems. Write your answers with complete solutions in 1 whole sheet of paper. 1.
A population consists of the five measurements 2, 6, 8, 0, and 1. a. What is the mean and standard deviation of the population? b. What is the mean of the sampling distribution of the sample means? c. What is the standard deviation of the sampling distribution of the sample means?
2.
Given the population 1, 3, 4, 6, and 8. Suppose samples of size 3 are drawn from this population. a. What is the mean and standard deviation of the population? b. What is the mean of the sampling distribution of the sample means? c. What is the standard deviation of the sampling distribution of the sample means?
3.
A molding machine prepares a certain kind of car spare part with a target diameter = 40.27 millimeters. The machine has some variability, so the standard deviation of the diameters is = 0.004 millimeters. A sample of 6 spare parts is inspected each hour for process control purposes and records are kept of the sample mean diameter. What will be the mean and standard deviation of the numbers r ecorded?
4.
In 2015, the mean return of all common stocks on the Philippine Stock Exchange was 3.5%. The standard deviation of the returns was about 26%. A student of finance forms all possible portfolios that invested equal amounts in 5 of these stocks and records the return for each portfolio. This return is the average of the returns of the 5 stocks chosen. What are the mean and standard deviation of the portfolio returns?
5.
A random sample of n = 60 measurements is obtained from a population with sampling distribution for the sample means by computing the X and X.
6.
A random sample of n = 100 measurements is obtained from a population with with the sampling distribution for the sample m eans by computing the X and X.
7.
In a study of the life expectancy of 400 people in a certain geographic region, the mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 68 y ears?
8.
The number of driving miles before a certain kind of tire begins to show wear is on the average, 16 800 miles with a standard deviation of 3 300 miles. A car rental agency buys 36 of these tires for replacement purposes and puts each one on a different car. a. What is the probability that the 36 tires will average less than 16 000 miles until they begin to show wear? b. What is the probability that the 36 tires will average more than 18 000 miles until they begin to show w ear?
9.
Manufacturer of ball bearings claims that this product has a mean weight of 5.02 g and a standard deviation of 0.30 g. What is the probability that a random sample of 100 ball bearings will have combined weight: a. between 496 g and 500 g? b. more than 510 g?
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10. An electrical company claims that the average life of the bulbs it manufactures is 1 200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be: a. greater than 1 150 hours? b. less than 1 250 hours? c. between 1 150 and 1 250 hours?
