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Solved: Waiting in Line A Wendy’s manager performed a
Chapter 11, Problem 20AYU(choose chapter or problem)
Problem 20AYU
Waiting in Line A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows:
x |
P(x) |
0 |
0.011 |
1 |
0.035 |
2 |
0.089 |
3 |
0.150 |
4 |
0.186 |
5 |
0.172 |
6 |
0.132 |
7 |
0.098 |
8 |
0.063 |
9 |
0.035 |
10 |
0.019 |
11 |
0.004 |
12 |
0.006 |
(a) Verify that this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Compute and interpret the mean of the random variable X.
(d) Compute the standard deviation of the random variable X.
(e) What is the probability that eight people are waiting in line for lunch?
(f) What is the probability that 10 or more people are waiting in line for lunch? Would this be unusual?
Questions & Answers
QUESTION:
Problem 20AYU
Waiting in Line A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows:
x |
P(x) |
0 |
0.011 |
1 |
0.035 |
2 |
0.089 |
3 |
0.150 |
4 |
0.186 |
5 |
0.172 |
6 |
0.132 |
7 |
0.098 |
8 |
0.063 |
9 |
0.035 |
10 |
0.019 |
11 |
0.004 |
12 |
0.006 |
(a) Verify that this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Compute and interpret the mean of the random variable X.
(d) Compute the standard deviation of the random variable X.
(e) What is the probability that eight people are waiting in line for lunch?
(f) What is the probability that 10 or more people are waiting in line for lunch? Would this be unusual?
ANSWER:
Answer:
Step 1 of 3
Given, A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows:
x |
P(x) |
0 |
0.011 |
1 |
0.035 |
2 |
0.089 |
3 |
0.150 |
4 |
0.186 |
5 |
0.172 |
6 |
0.132 |
7 |
0.098 |
8 |
0.063 |
9 |
0.035 |
10 |
0.019 |
11 |
0.004 |
12 |
0.006 |
(a)
x |
P(x) |
0 |
0.011 |
1 |
0.035 |
2 |
0.089 |
3 |
0.15 |
4 |
0.186 |
5 |
0.172 |
6 |
0.132 |
7 |
0.098 |
8 |
0.063 |
9 |
0.035 |
10 |
0.019 |
11 |
0.004 |
12 |
0.006 |
SUM |
1 |
i) Each probabilities must be between 0 and 1
ii) The sum of the probabilities must be equal to 1.
(b)
