Solution: Simulation Use the probability distribution from a
Chapter 6, Problem 36E(choose chapter or problem)
Problem 36E
Simulation Use the probability distribution from Problem and a DISCRETE command for some statistical software to simulate 100 repetitions of the experiment. Approximate the mean and standard deviation of the random variable X based on the simulation. Repeat the simulation by performing 500 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?
Problem
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?
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