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

Answer:

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

Step-by-step 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 : $z=\frac{x-\mu}{\sigma}$

At x = 14

$z=\frac{14-15.50}{1.72}$

$z=-0.8720$

Refer the  z table for p value

P(x<14)=0.1922

At x = 16

$z=\frac{16-15.50}{1.72}$

$z=0.290$

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