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# Normal Distributions: purchase amounts by customers

Suppose it is known that the distribution 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 the store?

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

c. What is the probability that a randomly selected customer spends more than \$10 at the 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 customers are between these values.

#### Solution Preview

Please see attached file.

Suppose it is know that the distribution 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 the store?
Mean=M= \$25
Standard deviation =s= \$8
x= \$35
z=(x-M)/s= 1.25 =(35-25)/8
Cumulative Probability corresponding to z= 1.25 is= 0.8944
Or Probability corresponding to x< 35.00 is Prob(Z)= 0.8944 0r= 89.44%

Answer: 0.8944 0r 89.44%

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

Mean=M= \$25
Standard deviation ...

#### Solution Summary

The solution calculates probabilities using normal distribution.

\$2.19