Question

A local store finds that the mean purchase amount per customer is $73.24. Suppose the purchase amounts per customer are normally distributed with a standard deviation of $8.94. The z-score for a purchase amount of $57 is z=-1.82. Interpret this z-score.

a) The purchase amount of $57 is 1.82 means below the standard deviation of $8.94.

b) The purchase amount of $57 is 1.82 standard deviations below the mean of $73.24.

c) The purchase amount of $57 is 1.82 means above the standard deviation of $8.94.

d) The purchase amount of $57 is 1.82 standard deviations above the mean of $73.24.

Answer 1

Ans.

The correct option is B, i.e., The purchase amount of $57 is 1.82 standard deviation below the mean of $73.24.

As we know that the z-score is a standardized score which tells that, how far an observation from its won mean in terms of its standard deviation. z-scores have mean of 0 and a standard deviation of 1.

As we have given,

So, we can interpret this z-score as, "the purchase amount of $57 is -1.82 standard deviations below the mean purchase amount per customer of $73.24 ."