Abaker knows that the daily demand for strawberry pies is a random variable that follows the normal distribution with a mean of 31.8 pies and a standard deviation of 4.5 pies. find the demand that has an 8% probability of being exceeded.

A demand of 38.1225 pies has an 8% probability of being excedeed.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the demand that has an 8% probability of being exceeded:

This is the value of X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

A demand of 38.1225 pies has an 8% probability of being excedeed.

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