Math 3
Unit 1 Review for Test
Name _______________________________
1. The amount of time that Lenny plays Candy Crush in any given week is normally distributed. If Lenny
plays Candy Crush an average of 16 hours per week, with a standard deviation of 2 hours, what is the
probability of Lenny playing Candy Crush between 14 and 16 hours a week?
2. A group of 700 students has a mean age of 14.3 years with a standard deviation of 0.7 years. The ages
are normally distributed. What is the percentile of a 13 year old? Explain what it means.
3. A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative
ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20.
For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5.
Which is this person’s stronger ability: verbal or quantitative? Explain your answer.
4. Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find:
a) 𝑃(65 < 𝑋 < 80) =
b) 𝑃(𝑋 > 75) =
c) 𝑃(𝑋 < 62) =
d) 𝑃(𝑋 < 𝑥) =0.83
5. The number of children of each of the first 41 United States presidents has been recorded. For this
population, the mean number of children is 3.6 and the standard deviation is 2.9.
a. Find the probability of a president having more than 4 children.
b. How many children did a president have if he was in the 20th percentile?
6. Psychologists were interested in assessing the effect of commercials on eating behavior in children. They
randomly assigned a group of 500 children, 7-11 years old, to two groups. After randomization, each
child was asked to watch a cartoon in a private room, containing a large bowl of goldfish crackers. The
cartoon included 2 commercial breaks.
The first group watched food commercials (mostly snacks), while the second group watched non-food
commercials (games and entertainment products). Once the child finished watching the cartoon, the
psychologists weighed the crackers bowl to measure how many grams of crackers the child ate. Then,
they compared the average amount of crackers eaten by each group.
The psychologists found that the mean amount of crackers eaten by the children who watched food
commercials is 10 grams greater than the mean amount of crackers eaten by the children who watched
non-food commercials.
For a full explanation to this problem, check out:
https://www.khanacademy.org/math/probability/statistical-studies/hypothesis-test/v/statisticalsignificance-experiment
a.
What is the treatment and response variable of this experiment?
b. Using a simulator, they re-randomized the results into two new groups and measured the difference
between the means of the new groups. They repeated this simulation 150 times, and plotted the
resulting differences, as given below. Based on the re-randomization simulations of difference in
means below, is this study statistically significant? Show your work and explain your answer.
c. Who can the results of this experiment be generalized towards?
7. The histogram below shows the distribution of the daily high temperatures in Pittsburgh for 2010.
Notice the distribution is not quit normal.
a. What percent of the temperatures lie within one standard deviation of the mean?
b. What percent of the temperatures lie within one standard deviation above the mean?
8. The ages of the population of a town are normally distributed with mean 43 and standard deviation 14.
a. (Without a calculator) draw the distribution, make sure to label appropriate percentages and
scale the x-axis.
b. (Without a calculator) What percent of ages lie below 29?
c. (Without a calculator) What percent of ages are between 15 and 71?
d. (Without a calculator) What percent of ages lie more than 28 from the mean?
e. (Without a calculator) Mrs. Surdy is 29, what is her percentile in this town?
Additional information:
-Make sure you know the characteristics of a well designed experiment.
- Understand evaluator blind, subject blind and double blind.