Question

A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of

8 dollars.
What proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars?
You may round your answer to four decimal places.

Answer 1

The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099

Explanation:

A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of 8 dollars.

`Mean = \mu = 87`

Standard deviation =
`\sigma = 8`

We are supposed to find proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars i.e.P(104.60<x<108.20)

`Z=(x-\mu)/(\sigma)`

At x = 104.60

`Z=(104.60-87)/(8)`

Z= 2.2

At x=108.20

`Z=(108.20-87)/(8)`

Z= 2.65

Refer the z table for p value :

P(x<108.20)-P(x<104.60)=P(Z<2.65)-P(Z<2.2)=0.9960-0.9861=0.0099

Hence The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099