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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?

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.

$2.19