Test 2C - Mr. Myers' Mathletes



Test 2C AP Statistics Name:

Directions: Work on these sheets. A standard Normal table is attached.

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. The density curve shown to the right takes the value 0.5 on the interval 0 ≤ x ≤ 2 and takes the value 0 everywhere else. What percent of the observations lie between 0.5 and 1.2?

(a) 25%

(b) 35%

(c) 50%

(d) 68%

(e) 70%

2. The proportion of observations from a standard Normal distribution that take values greater than 1.15 is about

(a) 0.1251 (b) 0.8531 (c) 0.8729 (d) 0.8749 (e) 0.8770

3. If the median of a set of data is equal to the mean, then

(a) The data are Normally distributed.

(b) The data are approximately Normally distributed.

(c) The distribution is skewed.

(d) The distribution is symmetric.

(e) One can’t say anything about the shape of the distribution with any certainty.

4. The figure at the right is the density curve of a distribution:

Five of the seven points marked on the density curve make up the five-number summary for this distribution. Which two points are not part of the five-number summary?

(a) B and E.

(b) C and F.

(c) C and E.

(d) B and F.

(e) A and G.

5. If the heights of American men follow a Normal distribution, and 99.7% have heights between 5'0" and 7'0", what is your estimate of the standard deviation of the heights of American men?

(a) 1"

(b) 3"

(c) 4"

(d) 6"

(e) 12"

The figure below shows a Normal curve. Questions 6 and 7 refer to this figure.

[pic]

6. The mean of this distribution is

(a) 0 (b) 1 (c) 2 (d) 3 (e) 5

7. The standard deviation of this Normal distribution is

(a) 0 (b) 1 (c) 2 (d) 3 (e) 5

8. The average yearly snowfall in Chillyville is Normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation?

(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.

Part 2: Free Response

Answer completely, but be concise. Show your thought process clearly.

9. As part of the President’s Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit & reach, one-mile run, and pull-ups. The qualifying standards are based on the 1985 School Population Fitness Survey. For the Presidential award, the standard for each event is 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. To win either award, a student must meet the qualifying standard for all five events.

Jane, who is 9 years old, did 40 curl-ups in one minute. Matt, who is 12 years old, also did 40 curl-ups in one minute. The qualifying standard for the Presidential award is 39 curl-ups for Jane and 50 curl-ups for Matt. For the National award, the standards are 30 and 40, respectively.

(a) Compare Jane’s and Matt’s performances using percentiles. Explain in language simple enough for someone who knows little statistics to understand.

(b) Who has the higher standardized value (z-score), Jane or Matt? Justify your answer.

10. A Normal probability plot of the survival times of the guinea pigs in a medical experiment is shown below. Use this plot to describe the shape of the distribution of survival times. Then explain carefully how this shape is determined from the Normal probability plot.

[pic]

11. The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test that 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 showing more Anglo/English acculturation. The distribution of ARSMA scores in a population used to develop the test is approximately Normal with mean 3.0 and standard deviation 0.8. A researcher believes that Mexicans will have an average score near 1.7 and that first-generation Mexican Americans will average about 2.1 on the ARSMA scale.

(a) Sketch the density curve of this Normal distribution, with the scale clearly marked on the horizontal axis.

(b) What proportion of the population used to develop the test has scores between 1.7 and 2.1? Show your work.

(c) How high a score on this test must a Mexican American obtain to be among the 30% of the population used to develop the test who are most Anglo/English in cultural orientation? Show your method.

I pledge that I have neither given nor received aid on this test. ________________________

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