Suppose it is known that the distribution of purchase amounts by customers enter

Question

Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $75 and standard deviation $25.

a. What is the probability that a randomly selected customer spends less than $85 at this store?

b.  What is the probability that a randomly selected customer spends between $65 and $85 at this store

c. What is the probability that a randomly selected customer spends more than $45 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.

Explanation / Answer

a) Z= (85-75)/25 = 0.4

P(z>0.4) = 0.344578

b)Z1=0.4 , Z2=-0.4

P( <-0.4<z<0.4) = 1- 2* 0.344578= 0.3108

c) Z = (45-75)/25=-1.2

P(z>-1.2) = 1-0.11507= 0.88493

d) Z-value for 75% cumulative probability = 0.67449

Value = 75+25* 0.67449= 91.87

e)

Z-value for 75% cumulative probability = 0.841621

Value = 75+25*0.841621= 96.04

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