1
Chapter 5:
1) Flip a coin three times.
(a) Find the sample space.
(b) Let X be the number of tails. Find the probability distribution for X.
(c) Draw a graph for the distribution.
(d) Find the mean, variance and standard deviation for X.( No credits will be
given if you did not show your work.)
(e) Find the probability of getting at least one tail.
(f) Find the probability of getting at most two tails.
2) From past experience, a company has found that in cartons of transistors, 93%
contain no defective transistors, 4% contain one defective transistor, 2% contain
two defective transistors, and 1% contain three defective transistors.
(a) Find the mean defective transistors.
(b) About how many extra transistors per day would the company need to
replace the defective ones if it uses 25 cartons per day?
3) If Mary rolls doubles when she tosses two dice, she wins $5. For the game to be
fair, how much should Mary pay to play the game?
4) In a Gallup Survey, 90% of the people interviewed were unaware that maintaining
a healthy weight could reduce the risk of stroke. If 15 people are selected at
random,
(a) find the probability that at least 5 are unaware that maintaining a proper
weight could reduce the risk of stroke.
(b) Find the probability that exactly 7 are unaware that maintaining a proper
weight could reduce the risk of stroke.
5) In a restaurant, a study found that 42% of all patrons smoked. If the seating
capacity of the restaurant is 150 people.
(a) Find the mean, and standard deviation of the number of smokers.
(b) About how many seats should be available for smoking customers?
6) In a survey, 58% of American adults said they had never heard of the Internet. If
20 American adults are selected at random,
(a) find the probability that exactly 12 will say they have never heard of the
Internet.
(b) Find the probability that at least three will say they have never heard of the
Internet.
Answer
Chapter 5
2
5
0.11, 3
63, 6.04, 63 seats
Answer
1
3
6
$0.83
4
0.177, almost 1
Answer
HHH,HHT,HTH,THH,HTT,THT,
TTH,TTT; 1.5, 0.75, 0.87; 7/8, 7/8
Almost 1; 0.00003