14. The average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a standard deviation of 3.6 minutes. Assume the variable is normally distributed. When a patron arrives at the restaurant for dinner, find the probability that the patron will have to wait the following time

Incomplete question, but you use the normal distribution to solve it, with and

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a standard deviation of 3.6 minutes.

This means that

Thus

Find the probability that the patron will have to wait:

More than X minutes:

1 subtracted by the p-value of Z

Between A and B minutes:

p-value of Z when X = A subtracted by the p-value of Z when Z = B.

Less than X minutes.

p-value of Z.

180

step-by-step explanation:

4400

step-by-step explanation: