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HCS 438 Apprentice
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Chapter 2 Review
Basic Statistics
Test_B AP Statistics
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AP Statistics
Name:
Directions: Work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. The heights of American men aged 18 to 24 are approximately Normally distributed with m inches and standard deviation 2.5 inches. Half of all young men are shorter than (a) 65.5 inches (b) 68 inches (c) 70.5 inches (d) can’t tell, because the median height h eight is not given (e) none of the above
problem. Only about 5% of young men have heights 2. Use the information in the previous problem. the range (a) 65.5 inches to 70.5 inches (b) 63 inches to 73 inches (c) 60.5 inches to 75.5 inches (d) 58 inches to 78 inches (e) none of the above
3. For the density curve shown to the right, which statement is true? (a) The area under the curve between 0 and 1 is is 1. (b) The density curve is symmetric. (c) The density curve is skewed skewed right. (d) The density curve is Normal. (e) None of the above is correct.
Master your semester with Scribd Read Free Foron 30this Days Sign up to vote title & The4.New York Useful For the densityTimes curve shown in Question Question 3, which statement is true? Not useful Special offer for (a) students: Only $4.99/month. The mean and median are equal.
(b) The mean is greater than the median.
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Basic Statistics
Test_B AP Statistics
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Normal density curve has which of the following properties? 6. A Normal (a) It is symmetric. (b) It has a peak centered above its mean. (c) The spread of the curve is proportional to it standard deviation. (d) All of the properties (a) to (c) are correct. (e) None of the properties (a) to (c) is correct.
professional schools require require applicants to take a standardized test. Suppose that 1000 7. Many professional students take the test, and you find that your mark of 63 (out of o f 100) is the 73rd percentile. This means that (a) at least 73% of the people scored 63 or better. (b) at least 270 people scored 73 or better. (c) at least 730 people scored 73 or better. (d) at least 27% of the people scored 73 or worse. (e) at least 270 people scored 63 or better.
to be 8. The yield of a variety of wheat was measured on a series of small plots and was found to approximately Normal. The 2nd and 98th percentile were found to be 29 bushels/acre and 4 bushels/acre respectively. The standard deviation (bushels/acre) is approximately (a) 12 (b) 6 (c) 4 (d) 3 (e)
would be best approximated by a Normal distribution? distribution? 9. Which of the following histograms would (a) (b) (c)
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The figure below shows a Normal Normal curve. Questions 12 and 13 refer to this figure.
12. The mean of this distribution is (a) 0 (b) 1
(c) 2
13. The standard deviation of this Normal distribution is (a) 0 (b) 1 (c) 2
(d) 3
(e)
(d) 3
(e)
Normally distributed with a mean of 55 inches 14. The average yearly snowfall in Chillyville is Normally the snowfall in Chillyville exceeds 60 inches in 15 % of the years, what is the standard devi (a) 4.83 inches (b) 5.18 inches (c) 6.04 inches (d) 8.93 inches (e) The standard deviation cannot be computed from the given information.
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Part 2: Free Response Answer completely, but be concise. Show your thought process clearly.
15. As part of the President’s Challenge, students can attempt to earn the Presidential Physical Award or the National Physical Fitness Award by meeting qualifying standards in five even ups, shuttle run, sit & reach, one-mile run, and pull-ups. pull-ups. The qualifying standards are base 1985 School Population Fitness Survey. For the Presidential award, the standard standard for each e the 85th percentile of the results for a specific age group and gender among students who participated in the 1985 survey. For the National award, the standard is the 50th percentile win either award, a student must meet the qualifying standard for all five events. Jane, who is 9 years old, old, did 40 curl-ups in one minute. Matt, who is 12 years old, also curl-ups in one minute. The qualifying standard for the Presidential award is 39 curl-ups curl-ups fo and 50 curl-ups for Matt. Matt. For the National award, the standards standards are 30 and 40, respectively respectively (a) Compare Jane’s and Matt’s performances using percentiles. Explain in language simpl enough for someone who knows little statistics to understand.
Jane earned both awards because she was just above the 85th percentile. (Jane more curl ups than 85% of the females in her age group.) Matt earned the Nation award because he fell right at the 50 th percentile. (He did more curl ups than 50 males in his age group.) Matt did not earn the Presidential award.
(b) Who has the higher standardized value ( z-score), z-score), Jane or Matt? Justify your your answer.
Master your semester with Scribd bette Jane has a high z-score because she has a higher percentile and performed Read Free Foron 30 Days Sign up to vote this title relative their peers. & TheMatt New YorktoTimes Useful Not useful Special offer for students: Only $4.99/month.
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17. The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test t measures the degree to which Mexican Americans are adapted to Mexican/Spanish versus Anglo/English culture. The range of possible scores is 1.0 to 5.0, with higher scores showin Anglo/English acculturation. The distribution of ARSMA scores in a population used to dev the test is approximately Normal with mean 3.0 an d standard deviation 0.8. A researcher b that Mexicans will have an average score sco re near 1.7 and that first-generation Mexican Ameri will average about 2.1 on the ARSMA scale. (a) Sketch the density curve of this Normal distribution, with the scale clearly marked on th horizontal axis.
(b) What proportion of the population used to develop the test has scores between 1.7 and 2 Show your work.
Normalcdf(1.7, 2.1, 3, .8) = .078 7.8% of the population used the develop the test has scores between 1.7 and 2.1.
Master your semester with Scribd Read Free For 30this Days Sign obtain up to vote title the 30% of (c) How high a score on this test must a Mexican American to on be among & The New population York Times useful orientation? Useful inNot used to develop the test who are most Anglo/English cultural Special offer for students: $4.99/month. your Only method.
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Part 2: Free Response Answer completely, but be concise. Show your thought process clearly.
that the body temperature of a healthy person is 98.6°F. In reality, the actua 18. We all “know” that the temperature of individuals varies. Here are boxplots, produced by Minitab, for the body temperatures of 130 individuals (65 males and 65 females). Gender 1 2
*
*
*
Temps 96 . 0
97 . 2
98 . 4
99 . 6
1 00 . 8
(a) What do the boxplots suggest about the Normality of the distributions of temperatures temperatures f males (Gender = 1) and females (Gender = 2)? Give specific evidence to justify justify your a
The distribution of temperatures for males is slightly skewed left because the first quartile is spread spread out more than the others. distribution of temperatures for females is approximately normal because t quartiles are evenly spread out with 2 outliers at the low end and one at the end.
(b) According to Minitab, µ Minitab, µ = = 98.103 and = 0.700 for the male temperatures. temperatures. If we assum the males’ temperatures are Normally distributed, what percent would have temperature 98.7 degrees or above? Show your work.
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19. The best male long jumpers for State College since 1973 have jumped an average of 26 inches with a standard deviation of 14.0 inches. The best female long jumpers have averag 201.2 inches with a standard deviation deviation of 7.7 inches. This year Joey jumped 275 inches sister, Carla, Carla, jumped 207 inches. Both are State College students. (a) Find the standardized values for Joey’s and Carla’s jumps. Which athlete had the more impressive performance? Explain briefly.
Joey’s performance was more impressive because he jumped further relative to other male long jumpers at State College than Carla jumped relative to the females. (b) Assume that male and female jumps are Normally distributed. distributed. Find the percentiles for and Carla’s jumps. jumps. Interpret these percentiles in context.
Joey’s jump is at 80 th percentile. He jumped further further than 80% of males at Stat College.
females a Carla’s jump is at the 77 th percentile. She jumped further than 77% of females State College.
c ertain female populati 20. The length of pregnancies from conception to natural birth among a certain Normally distributed with mean 270 days and standard deviation 10 days. (a) According to the 68 – 95 95 – 99.7 99.7 rule, what percent of pregnancies last more than 300 days your method and explain your answer.
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(b) How Ho w short must a pregnancy be in order to fall fall in the shortest 10% of all pregnancies?
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