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AP Statistics
Chapter 6 – Random Variables
Winter Break Worksheet
Name _________________________________________
Section 1 – Random Variables!!!!
1.)
a.) What is the probability that a random patient will need more than 3 tests?
b.) What is the probability a random patient will need at least 1 test?
c) Use your calculator to find the mean (or expected) amount of medical tests a random patient would receive
and with what standard deviation.
d.) Explain what the mean (or expected) amount means.
2.) The mean height of players in the NBA is about 79 inches and the standard deviation is 3.5 inches.
Assume the distribution of heights is approximately Normal. Let H be the continuous random variable for the
height of a randomly selected NBA player.
a.) Explain why H is a continuous random variable and not a discrete random variable.
b.) Draw a picture of this Normal distribution labeled properly with the heights.
c.) Use your calculator to find the probability that a randomly selected player is less than 74 inches tall, which
can be expressed as P(H < 74).
d.) Use your calculator to find the probability that a randomly selected player is greater than 88 inches tall,
which can be expressed as P(H > 88).
3.)
Create a probability model for T and find the mean (or expected) value and standard deviation for T.
Section 2 – Combining Random Variables
1.)
2.) Suppose that the mean height of policemen is 70 inches with a standard deviation of 3 inches. And
suppose that the mean height for policewomen is 65 inches with a standard deviation of 2.5 inches. Assume
the heights of policemen and policewomen are Normally distributed.
a.) Two random policemen are paired up to be partners. Let P = the total height of the two policemen. What is
the mean (or expected value) and the standard deviation for P?
b.) A policeman and a policewoman are to be paired up to be partners. Let T = the total height of the
policeman and policewoman. What is the mean (or expected value) and the standard deviation for T?
c.) What is the probability that T (the total height for a policeman and policewoman) is less than 127 inches?
This can be denoted as P(T < 127).
d.) What is the probability that a randomly selected policewomen is taller than a randomly selected policeman?
Section 3 – Binomial and Geometric Models
1.) It is known that 11% of people have Type O blood. Assume a person’s blood type is independent of
another person’s. Consider a blood drive with many people coming in to donate blood.
This first set of questions are Geometric based:
a.) What is the probability the FIRST person you find with type O blood is the 7th person who donates?
b.) What is the probability that the FIRST person to have Type O blood is after the 3rd person?
c.) How many people do you expect to see to get your FIRST person with Type O blood?
This second set of questions are Binomial based:
d.) Assume you have a group of 6 people. Create a probability model for X = the amount of people that have
type O blood. Show all work to calculate the probability of each possible outcome.
e.) How many people in the group of 6 do you expected to have type O blood and with what standard
deviation?
2.)