Question

The mean number of pairs of shoes sold by a shoe store is 36, with a standard deviation of 3. On what percent of days would you expect the store to sell from 33 to 42 pairs of shoes?

a. 13.5%
b. 50%
c. 68%
d. 81.5%

Answer 1

81.85% of days would you expect the store to sell from 33 to 42 pairs of shoes

Explanation:

The mean number of pairs of shoes sold by a shoe store is 36

`\mu = 36`

Standard deviation =
`\sigma = 3`

We are supposed to find percent of days would you expect the store to sell from 33 to 42 pairs of shoes i.e.P(33<x<42)

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

At x = 33

`Z=(33-36)/(3)`

Z=-1

Refer the z table for p value

p =0.1587

At x = 42

`Z=(42-36)/(3)`

Z=2

Refer the z table for p value

p =0.9772

So,P(33<x<42)=P(x<42)-P(x<33)=0.9772-0.1587=0.8185

Hence 81.85% of days would you expect the store to sell from 33 to 42 pairs of shoes