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CP Statistics 8.1: Binomial Random Variables – Worksheet 3
Explain whether the given random variable has a binomial distribution.
1. Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the company’s claim is
true. Judy buys a packet of 30 seeds from Seed Depot and plants them in her garden. Let X = the number of
seeds that germinate.
2. Put the names of all of the students in your statistics class in a hat. Mix them up, and draw four names without
looking. Let Y = the number whose last names have more than six letters.
3. Exactly 10% of the students in a school are left-handed. Select students at random from the school, one at a
time, until you find one who is left-handed. Let V = the number of students chosen.
4. Exactly 10% of the students in a school are left-handed. Select 15 students at random from the school and
define W = the number who are left-handed.
Use the binomial probability formula (and online calculator) to answer the following.
5. In the United States, 44% of adults have type O blood. Suppose we choose 6 US adults at random. What is the
probability that…
a. Exactly 4 of them have type O blood?
b. Two or fewer have type O blood?
c. More than 4 of them have type O blood?
6. Suppose that exactly 10% of the students at your school are left-handed. You randomly select 15 students at
your school.
a. What is the probability that exactly 3 of them are left-handed?
b. Would you be surprised if 4 or more of the students were left-handed? Calculate P(Y≥4) and use this
result to support your answer.
c. What is the mean number of students expected to be left-handed in your sample?
7. As a special promotion, a soft-drink company prints a message inside the cap of each of its 20-oz bottles of soda.
Some say “try again” while others say “winner” and that person wins a prize. The company advertises that 1 in 6
bottles wins a prize. Seven friends each buy a bottle of this soda at a local convenience store. Let X = the number
who win a prize.
a. The store clerk is surprised when three of these friends win a prize. Calculate the probability of this
occurrence. Should he be surprised?
b. What is the probability that fewer than 3 of the friends would win a prize?
c. What is the probability that 3 or more of them win a prize?