Question

Average sales for an online textbook distributor were $67.63 per customer per purchase. Assume the sales are normally distributed. If the standard deviation of the amount spent on textbooks is $8.96, find these probabilities for a randomly selected customer of the online textbook distributor. Round your answer to the nearest tenth of a percent. (a)He or she spent more than $85.55 per purchase. (b)He or she spent less than $76.59 per purchase

Answer 1

(a)P(x>85.55)=0.02275

(b)
`P(x<76.59)=0.84134`

Explanation:

We are given that

Average sales for an online textbook distributor per customer per purchase

,
`\mu=`$67.63

Standard deviation of the amount spent on textbooks,
`\sigma=`$8.96

(a) We have to find probability for a randomly selected customer spent more than $85.55 per purchase.

`P(x>85.55)=P((x-\mu)/(\sigma)>(85.55-67.63)/(8.96))`

=
`P(Z>2)`

=
`1-P(Z\leq 2)`

=
`1-0.97725`

P(x>85.55)=0.02275

(b)We have to find probability for a randomly selected customer spent less than $76.59 per purchase

`P(x<76.59)=P((x-\mu)/(\sigma)<(76.59-67.63)/(8.96))`

`P(x<76.59)=P(Z<1)`

`P(x<76.59)=0.84134`