Download Math 3 Name__________________ 1.

Math 3
Name__________________
1.
The distribution of SAT scores in a reference population is normally distributed
with mean 500 and standard deviation 100. Sketch the density curve of the
distribution going out three standard deviations to the left and right of the mean.
2.
Jill scores 680 on the SAT. Find the standardized score and relative frequency
(her percentile).
3.
The distribution of ACT scores in a reference population is normally distributed
with mean 18 and standard deviation 6. Sketch the density curve of the
distribution going out three standard deviations to the left and right of the mean.
4.
Jack scores 27 on the ACT. Find the standardized score and the relative
frequency (his percentile).
5.
Assuming that the ACT and SAT measure the same kind of ability, who has the
higher score, Jack or Jill. How do you know?
Using Table A, find the proportion of observations from a standard normal distribution
that satisfies each of the following statements. In each case, draw a normal curve and
shade the area under the standard normal curve that is the answer to the question.
6. z < -1.5
7. –1.5 < z < .8
8. The distribution of grades for a statistics class is normal with a mean of 75 and
standard deviation of 7. What score would a student need to be in the top 10% of the
class?
A lunch stand in the business district has a mean daily gross income of $420 with a
standard deviation of $50. Assume that daily gross incomes are normally distributed.
9.
If a randomly selected day has a gross income of $520, then how many standard
deviations away from the mean is that day’s gross income?
10.
Determine the standardized value for a daily income of $495.
11.
What relative frequency (percentile) corresponding to a daily gross income of
$495 or more.
The scores of a reference population on the Wechsler Intelligence Scale for Children
(WISC) are normally distributed with  X  100 and  X  15.
12.
Sketch the density curve. Then label the mean, and 1, 2, and 3 standard
deviations from the mean.
13.
Approximately what percent of the scores fall in the range from 70 to 130?
14.
A score in what range would represent the top 16% of the scores?
15. Runner’s World reports that the times of the finishers in the New York City 10-km
run are normally distributed with a mean of 61 minutes and a standard deviation of 9
minutes.
a. Find the percent of runners who take more than 70 minutes to finish.
b. Find the percentage of runners who finished in less than 43 minutes.
16. The best male long jumpers for State College since 1973 have averaged a jump of
263 inches with a standard deviation of 14 inches. The best female long jumpers have
averaged 201.2 inches with a standard deviation of 7.7 inches. This year Joey jumped
275 inches and his sister, Carla, jumped 207 inches. Both are State College students.
Assume that the lengths are approximately normal. Within their groups, which athlete
had the more impressive performance? Show your work.
17. The next year a freshman at State College jumped and was in the 45th percentile.
How long was the jump?
18. The next year they improved to the 85th percentile, how long was the jump in their
sophomore year?
19. What percentage of jumpers lie between their freshman and sophomore year.