A study of drive-thru wait times for fast-food restaurants found that the average time spent Wendy's drive-thru was 138.5 seconds. Assume that drive-thru wait times are normally distributed with a standard deviation of 29 seconds, A Wendy's owner wants to give a free Frosty to customers who have an unusually long wait in the drive-thru. The length of time the owner should choose so that only 0.75% of customers get a free Frosty i. e. only 0.75% wait longer than seconds) is seconds (give your answer to 2 decimal places).

207.72 seconds.

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.

Mean waiting time of 138.5 seconds, standard deviation of 29 seconds.

This means that

The length of time the owner should choose so that only 0.75% of customers get a free Frosty i.e. only 0.75% wait longer than

The 100 - 0.75 = 99.15th percentile, which is X when Z has a pvalue of 0.9915, so X when Z = 2.387.

So the answer is 207.72 seconds.

step-by-step explanation:

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step-by-step explanation: