Homework Sourse20 Waiting in Line A Wendys manager performed a study to det
20. 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:
(a) Verify that this is a discrete probability distribution.
Answer:
(c) Compute and interpret the mean of the random variable X.
Answer:
(d) Compute the standard deviation of the random variable X.
Answer:
(e) What is the probability that eight people are waiting in line for lunch?
Answer:
| 20. 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: |
| (a) Verify that this is a discrete probability distribution. |
| Answer: |
| (c) Compute and interpret the mean of the random variable X. |
| Answer: |
| (d) Compute the standard deviation of the random variable X. |
| Answer: |
| (e) What is the probability that eight people are waiting in line for lunch? |
| Answer: |
Solution
Consider this table:
x P(x) x P(x) x^2 P(x)
0 0.011 0 0
1 0.035 0.035 0.035
2 0.089 0.178 0.356
3 0.15 0.45 1.35
4 0.186 0.744 2.976
5 0.172 0.86 4.3
6 0.132 0.792 4.752
7 0.098 0.686 4.802
8 0.063 0.504 4.032
9 0.035 0.315 2.835
10 0.019 0.19 1.9
11 0.004 0.044 0.484
12 0.006 0.072 0.864
Sum P(x) = 1
Sum [xP(x)] = 4.87
Sum [x^2 P(x)] = 28.686
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a)
We verified that it is a discrete probability distribution as the sum of the probabilities is 1.
c)
Mean = Sum [x P(x)] = 4.87
d)
s = sqrt [Sum (x^2 P(x)) - Sum(x)^2]
= sqrt[28.686 - 4.87^2]
= 2.229147819 [answer]
e)
From the table, P(8) = 0.063 [answer]
