Question

The distribution of the amount of a customer’s purchase at a convenience store is approximately normal, with mean $15.50 and standard deviation $1.72. Which of the following is closest to the proportion of customer purchase amounts between $14.00 and $16.00 ?

A) 0.19
B) 0.39
C) 0.42
D) 0.61
E) 0.81

Answer 1

C

Explanation:

Find the z-scores for both $14 and $16, then find the area that is between both of the values which should be 0.42

Answer 2

0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00

Explanation:

Mean =
`\mu = 15.50`

Standard deviation =
`\sigma = 1.72`

We are supposed to find the proportion of customer purchase amounts between $14.00 and $16.00

P(14<x<16)

Formula :
`z=(x-\mu)/(\sigma)`

At x = 14

`z=(14-15.50)/(1.72)`

`z=-0.8720`

Refer the z table for p value

P(x<14)=0.1922

At x = 16

`z=(16-15.50)/(1.72)`

`z=0.290`

Refer the z table for p value

P(x<16)=0.6141

P(14<x<16)=P(x<16)-P(x<14)=0.6141-0.1922=0.42

So, Option C is true

Hence 0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00