Sec. 6.3: Binomial & Geometric Distribution Review
Name:________________________
1. An inspection procedure at a manufacturing plant involves picking three items at random and then accepting
the whole lot if at least two of the three items are in perfect condition. If in reality 84 percent of the whole lot
are perfect, what is the probability that they lot will be accepted?
What type of distribution should we use?__________________________
(a) 0.560
(b) 0.593
(c) 0.667
(d) 0.706
(e) 0.931
p = _________
2. Suppose a manufacturer knows that 20 percent of the circuit boards coming off the assembly line have a
minor defect. If an inspector keeps inspecting boards until he comes upon one with the defect, what is the
probability he will have to inspect at most three boards?
What type of distribution should we use?__________________________
(a) 0.128
(b) 0.384
(c) 0.488
(d) 0.512
(e) 0.896
p = _________
12 
k
12  k
3. Suppose we have a random variable X where the probability associated with the value k is   .34  .66 
k
For k = 0, 1, …, 12. What is the mean of X?
What type of distribution should we use?__________________________
(a) 0.34
(b) 0.66
(c) 4.08
(d) 7.92
(e) None of the above
p = _________
4. A person has a 10 percent chance of winning the daily office lottery. What is the probability she first wins
on the fourth day?
What type of distribution should we use?__________________________
 4
(a)   .10 3 .90 
1 
 4
3
(b)   .10 .90 
3
(c)
.10  .90 
3
(d) .10 .90 
3
(e) None of the above gives the correct probability.
p = _________
5. It is estimated that 20 percent of all drivers do not signal when changing lanes. In a random sample of four
drivers, what is the probability that at least one doesn’t signal when changing lanes?
What type of distribution should we use?__________________________
(a) 1  .2 
4
(b) 1  .8 
4
(c) 4 .2 .8 
p = _________
3
(d) 4 .2  .8 
3
(e) 4 .2  .8   6 .2  .8   4 .2 .8   .8 
3
2
2
3
4
6. A mortgage company advertises that 85 percent of applications are approved. In a random sample of 30
applications, what is the expected number that will be turned down?
What type of distribution should we use?__________________________
p = _________
(a) 30(.85)
(b) 30(.15)
(c) 30(.85)(.15)
(d) 30 .85.15
(e)
.85.15 
30
7. Suppose we have a binomial random variable where the probability of exactly four successes is  n  4
7.
p
.37




What is the mean of the distribution?
 4
p = _________
(a)
(b)
(c)
(d)
(e)
2.52
2.59
4.07
4.41
6.93
8. For which of the following is a binomial an appropriate model?
(a) The number of heads in ten tosses of an unfair coin weighted so that heads comes up twice as often as
tails.
(b) The number of hits in five at-bats where the probability of a hit is either .352 or .324 depending upon
whether the pitcher is right-handed or left-handed.
(c) The number of tosses of a fair coin before heads appears on two consecutive tosses.
(d) The number of snowy days in a given week.
(e) The binomial is appropriate for all of the above.
Multiple Choice Answers: 1. E, 2. C, 3. C, 4. D, 5. B, 6. B, 7. E, 8. A
9. In a certain lake, 65% of fish caught are thrown back. Consider catching 10 fish from the lake. Assume that
the fish you caught can be considered a random sample of all fish that are caught at the lake.
a. How many do you expect to throw back?
b. What is the probability that you keep more than 6 of the fish?
c. What is the probability that you get 2 or fewer “keepers” in the group?
d. What is the standard deviation?
10. Freecell is a popular solitaire card game. Jim plays frequently and has become quite good at it. In fact, he
wins 85% of the time. Suppose he decides to play until “his luck runs out.”
a. Define a random variable that could be used in this situation. Check its conditions.
b. What is the probability that he plays exactly three games?
c. What is the probability that he plays fewer than three games?
d. What is the probability that he plays more than three games?
e. Jim’s longest winning streak was 9 games in a row. What is the probability that Jim will lose before he
reaches 9 games again?
11. Suppose that x is a binomial random variable with n = 100 and p = 0.18. Verify that the rule of thumb
works to use normal approximation. Then, use normal approximation to find the probability that x is between
17 and 19.
12. The probability that Barry Bonds hits a homer on any given at-bat is .12, and each at-bat is independent.
(Hint: Be careful of which distribution you are using. Read carefully.)
a. What is the probability the next homer will be on his fifth at-bat?
b. What is the probability that he has exactly one homer in five at-bats?
c. What is the expected number of homers in every ten at-bats?
d. What is the expected number of at-bats until the next homer?
13. You are planning a sample survey of businesses in your area. You will choose an SRS of businesses listed
in the telephone’s Yellow Pages. There are 4200 businesses listed in the telephone’s Yellow Pages. Experience
shows that only about half the businesses you contact will respond.
a. If you contact 150 businesses, it is reasonable to use the binomial distribution with n = 150 and p = 0.5
for the number X who respond. Explain why.
b. What is the expected number (the mean) who will respond?
c. What is the probability that 70 or fewer will respond? (Use the normal approximation.)
d. How large a sample must you take to increase the mean number of respondents to 100?