# Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.

Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.

a) What is the probability that a randomly selected customer spends less than $35 at this store?

b) What is the probability that a randomly selected customer spends between $15 and $35 at this store?

c) What is the probability that a randomly selected customer spends more than $10 at this store?

d) Find the dollar amount such that 75% of all customers spend no more than this amount?

e) Find the dollar amount such that 80% of all customers spend at least this amount?

f) Find two dollar amounts, equidistant from the mean of $25, such that 90% of all customer purchases are between these values?

https://brainmass.com/statistics/normal-distribution/159842

#### Solution Preview

Please see the attached file.

Suppose the purchase amount is X. Then the mean of X is m=25 and the standard deviation of X is d=8

Now let Y=(X-25)/8, then Y follows the standard normal distribution and X=8Y+25.

The following calculation will be done by the normal standard ...

#### Solution Summary

Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.