Binomial Distribution
Name_______________________
1. Eric teaches ceramics in his studio. He estimates that one out of every five people who call
for information about a class will sign up for the class. Last week he received nine calls.
Find the probability that four or fewer of the people who called will sign up for a class.
2. In Summit County 65% of the voter population are Republicans. What is the probability that
a random sample of ten Summit County voters will contain:
a. Exactly eight Republicans?
b. More than eight Republicans?
c. All Republicans?
3. Dorothy leads wilderness expeditions. She has found that 15% of those who attend a
promotional meeting will sign up for an expedition at the meeting. If 20 people attend a
meeting;
a. What is the probability that none of them will sign up?
b. What is the probability that exactly three of them will sign up?
c. What is the probability that at most four will sign up?
4. A TV sports commentator claims that 40% of all football injuries are knee injuries.
Assuming that this claim is true, what is the probability that in a game with 5 reported
injuries:
a. None are knee injuries?
b. All are knee injuries?
c. At least three are knee injuries?
d. No more than 2 are knee injuries?
5. The college health center did a campus-wide survey of students and found that 30% of the
students smoke cigarettes. A group of nine students randomly come together and sit at the
same table on the plaza in front of the library. Find the probability that:
a. At least one student at the table smokes?
b. At least three students smoke?
6. A safety engineer claims that 18% of all automobile accidents are due to mechanical failure.
Assume that this is correct and find the probability that exactly three out of eight
automobile accidents is due to mechanical failure?
7. Martha estimates that she will receive at least one marketing telephone call at home during
the hours of 5 pm to 7 pm on a weekday night to be 23 . What is the probability that she will
receive a call on at least four of the next five weekday nights?
8. It is estimated that 80% of patients who have an artery bypass heart operation survive
eight years without needing another bypass operation. Of seven patients who recently had
such an operation, what is the probability that more than five will survive eight years without
needing another bypass operation?
9. The probability of an adverse reaction to a pnuemonia shot is 0.15. These shots are given to
a group of 12 people.
a. What is the probability that at least one will have an adverse reaction?
b. What is the probability that more than half of them will have an adverse reaction to the
shot?
10. The probability that a restaurant patron will request seating in the outdoor patio is 0.45. A
random sample of 7 people call to make reservations. What is the probability that exactly 3
will call to request outdoor seating?
11. A fair quarter is flipped four times. What is the probability of getting fewer than two
heads?