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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

Respuesta :

Answer:

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

Step-by-step explanation:

Mean = [tex]\mu = 15.50[/tex]

Standard deviation = [tex]\sigma = 1.72[/tex]

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

P(14<x<16)

Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex]

At x = 14

[tex]z=\frac{14-15.50}{1.72}[/tex]

[tex]z=-0.8720[/tex]

Refer the  z table for p value

P(x<14)=0.1922

At x = 16

[tex]z=\frac{16-15.50}{1.72}[/tex]

[tex]z=0.290[/tex]

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

Answer:

C

Step-by-step 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

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