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Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III
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Waiting in Line A Wendys manager performed a study to determine a probability

Chapter 6, Problem 20

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QUESTION:

Waiting in Line A Wendys 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) x P(x) 0 0.011 7 0.098 1 0.035 8 0.063 2 0.089 9 0.035 3 0.150 10 0.019 4 0.186 11 0.004 5 0.172 12 0.006 6 0.132 (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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QUESTION:

Waiting in Line A Wendys 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) x P(x) 0 0.011 7 0.098 1 0.035 8 0.063 2 0.089 9 0.035 3 0.150 10 0.019 4 0.186 11 0.004 5 0.172 12 0.006 6 0.132 (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:

Step 1 of 6

(a)

 The distribution is discrete, because can only take on defined separate values .

The distribution is a valid probability distribution, if all probabilities are between 0 and 1 (including) and the sum of all probabilities is

We note that all given probabilities  are between 0 and 1 .

The sum of all probabilities is also l, thus the distribution is a valid probability distribution.

 

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