A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600. On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score. What is the percentile rank of sales for this day

Tuesday's z-score was of -1.325.

The percentile rank of sales for this day was the 9.25th percentile.

Step-by-step explanation:

Z-score:

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.

A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600.

This means that

On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score.

This is Z when X = 16230. So

Tuesday's z-score was of -1.325.

What is the percentile rank of sales for this day

This is the p-value of Z = -1.325.

Looking at the z-table, this is of 0.0925, and thus:

The percentile rank of sales for this day was the 9.25th percentile.

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step-by-step explanation: