# Question

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?

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?

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