6 if your score on a test is at the 60th percentile

6. If your score on a test is at the 60th percentile, you know that your score lies
(a) below the first quartile.
(b) between the first quartile and the median.
(c) between the median and the third quartile.
(d) above the third quartile.
(e) There is not enough information to say where it lies relative to the quartiles.
2
0
1
0.5

7. In some courses (but certainly not in an intro stats cours e!), students are graded on a ―Normal
curv e.‖ For example, students within ± 0.5 standard deviations of the mean receive a C;
between 0.5 and 1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5
standard deviations above the mean receive a B – ; between 1.5 and 2.0 standard deviations
above the mean receive a B, etc. The class average on an exam was 60 with a standard
deviation of 10. The bounds for a B – grade and the percent of students who will receive a B –
grade if the marks are actually Normally distributed are
8. The mean age (at inauguration) of all U.S. Presidents is approximately Normally distributed
with a mean of 54.6. Barack Obama was 47 when he was inaugurated, which is the 11
th
percentile of the distribution. Which of the following is closest to the standard deviation of
presidents’ ages?
9. Which of the following is not true about all Normal distributions? 10. The 16
th
percentile of a Normally distributed variable has a value of 25 and the 97.5
th
percentile has a value of 40. Which of the following is the best estimate of the mean and
standard deviation of the variable?
(a) Mean ≈ 32.5; Standard deviation ≈ 2.5
(b) Mean ≈ 32.5; Standard deviation ≈ 5
(c) Mean ≈ 32.5; Standard deviation ≈ 10
(d) Mean ≈ 30; Standard deviation ≈ 2.5
(e) Mean ≈ 30; Standard deviation ≈ 5
© 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 2 85

86 The Practice of Statistics, 4/e- Chapter 2 © 2011 BFW Publishers
Part 2: Free Response
Show all your work. Indicate clearly the methods you use, because you will be graded on the
correctness of your methods as well as on the accuracy and completeness of your results and
explanations.
Raw scores on behavioral tests are often transformed for easier comparison. A test of reading
ability has a mean of 75 and a standard deviation of 10 when given to third-graders. Sixth-
graders have a mean score of 82 and a standard deviation of 11 on the same test.