AIG Name: __________________________
Data Analysis Unit Part 1 Review – KEY Date: ___________ Period: ____
SHOW ALL WORK AND ANSWERS ON SEPARATE PAPER.
Topics for Data Analysis Unit Part 1 Test
Discrete Random Variables Percentiles
Binomial Distribution Normal Distribution
Continuous Random Variables Empirical Rule
Z-Scores Normal Probability Calculations
1. The probabilities that a randomly selected customer purchases 1, 2, 3, 4, 5, or 6 items at a convenience store are 0.24,
0.18, 0.26, 0.15, 0.11, and 0.06 respectively.
(a) Identify the random variable of interest. X = # items purchased. Then construct a probability distribution and
draw a probability distribution histogram. What is the shape of this distribution?
X = # items purchased 1 2 3 4 5 6
P(X) 0.24 0.18 0.26 0.15 0.11 0.06
Shape of P(X) = skewed right
(b) Describe in words the event 2 4) = 0.17
(d) What is the probability that a customer purchases no more than 2 items?
P(X 10) ≈ 0
(e) What is the probability that you draw fewer than 4 green marbles?
P(X < 4) = 0.69
(f) Calculate the mean X and the standard deviation X . Show your work.
Mean = 2.8 Standard deviation = 1.5
4. The distribution of the weights of loaves of bread from a certain bakery follows approximately a Normal distribution.
Based on a very large sample, it was found that loaves with a weight of 14.96 ounces had a z-score of –1.28, and
loaves with a weight of 16.82 ounces had a z-score of 0.84. What are the mean and standard deviation of the
distribution of the weights of the loaves of bread?
Mean = 16.09 Standard deviation = 0.88
5. The distribution below gives the IQ scores of 74 seventh-grade students. This distribution is approximately Normal
with a standard deviation of 11. Interpret this distribution as a description of IQ test scores for all seventh-grade
students. Find the mean and then use the Empirical Rule to answer the following questions.
8 6 9
9 0 1 3 3
9 6 7 7 8
10 0 0 2 2 3 3 3 3 4 4
10 5 5 5 6 6 6 7 7 7 7 8 9
11 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4
11 5 5 6 8 8 9 9 9
12 0 0 3 3 4 4
12 6 7 7 8 8 8
13 0 2
13 6
(a) Between what values do the IQ scores of 95% of seventh-grade students lie?
95% of seventh graders have IQ scores between 89 and 133.
(b) What percent of IQ scores for seventh-graders are greater than 100?
84% of seventh-graders have IQ scores greater than 100.
(c) What percent of IQ scores for seventh-graders are between 89 and 144?
97.35% of seventh-graders have IQ scores between 89 and 144.
AIG Data Analysis Unit Part 1 Review – KEY
SHOW ALL WORK AND ANSWERS ON SEPARATE PAPER.
6. The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the
combined mathematics and verbal parts of the SAT exam in order to compete in their first college year (Higher scores
are required for students with poor high school grades.) In 1999, the scores of the millions of students taking the SATs
were approximately Normal with mean 1017 and standard deviation 209.
(a) What percent of all students had scores less than 820?
17.36% of all students had scores less than 820.
(b) What percent of all students had scores between 800 and 1200?
66.14% of all students had scores between 800 and 1200.
(c) What percent of all students had scores greater than 1400?
3.36% of all students had scores greater than 1400.
7. It is possible to score higher than 800 on either part of the SAT, but scores above 800 are reported as 800. (That is, a
student can get a reported score of 800 without a perfect test.) In 1999, the scores of men on the math part of the SAT
followed a Normal distribution with mean 531 and standard deviation 115.
(a) What percent of male math scores were above 800 (and so reported as 800)?
0.96% of male math scores were above 800.
(b) What scores make up the top 10% of male math scores?
The top 10% of male math scores are 678.2 and higher.
(c) What scores make up the central 85% of male math scores?
The central 85% of male math scores are between 365.4 and 696.6.
8. The average performance of women on the SAT, especially the math part, is lower than that of men. The reasons for
this gender gap are controversial. In 1999, women’s scores on the math SAT followed a Normal distribution with mean
495 and standard deviation 109. The mean for men was 531.
(a) What percent of women scored higher than the male mean?
37.07% of women scored higher than the male mean.
(b) What scores make up the bottom 15% of female math scores?
The bottom 15% of female math scores are 381.64 and below.
(c) What scores make up the central 60% of female math scores?
The central 60% of female math scores are between 403.44 and 586.56.