AP Statistics
Uniform, Unique & Sampling Distributions
Name: ____________________________
1. Birth weights of infants at a local hospital have a normal distribution with a mean of 110 oz.
and a standard deviation of 15 oz.
a. What percentage of infants weigh between 100 oz. and 125 oz. at birth?
b. What percentage of infants weigh more than 160 oz. at birth? (that’s 10 lbs)
c. What birth weight corresponds to the 65th percentile?
2. Scores on the SAT-I test are normally distributed with a mean of 1017 and a standard
deviation of 209.
a. What proportion of students who take the test score above 1310?
b. The director of admissions for a junior college in Mississippi wants to admit as many
students as possible, but knows that his college is not right for all students. Therefore,
he decides that he will not admit students who score in the lower 4% or the upper 4%
on the SAT. What are the cutoff scores on the SAT for admission to this college?
3. The mean life span of a brand name tire is 50,000 miles. Assume that the life spans of the tires
are normally distributed, and the population standard deviation is 800 miles.
a. If you select one tire, what is the probability that its life span is less than 48,500 miles?
b. If you select 100 tires, how many tire will have a life span of more than 50,200 miles?
4. The ages of subscribers to the Monon Daily newspaper are normally distributed with a mean
of 35.5 years and a standard deviation of 4.8. (Source: Fundamentals of
Probability,Ghahramani)
a) What is the percentage of subscribers that are more than 35.5 years?
b) What is the percentage of subscribers between 30 and 40 years?
5. Heights of adult women are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. Men have an average height of 69.3 and a standard deviation of 2.8.
a) Find the standard score (z-score) and percentile for each of the following heights:
Woman 65 inches
Woman 63 inches
b) What is the percentage of women between 63 and 65 inches.
c) What is your height? _____ Find the z-score and percentile for your height and
interpret.
AP Statistics
Uniform, Unique & Sampling Distributions
Name: ____________________________
For problems 6 & 7, use the following Uniform Distribution for the following questions
f(x)
5
10
15
Salad Weight (oz.)
6. What is the probability that a customer will take between 12 and 15 ounces of salad?
7. What is the probability that a customer will take between 7 and 11 ounces of salad?
8. After completing a study, a company in Kansas City concluded the time its employees spend
commuting to work each day is normally distributed with a mean equal to 15 minutes and a standard
deviation equal to 3.5 minutes. One employee has indicated that she commutes 22 minutes per day.
Find the probability that an employee would commute 22 or more minutes per day.