Question

Assume the average price for a movie is $8.03. Assume the population standard deviation is $0.55 and that a sample of 40 theaters was randomly selected. Complete parts a through d below.

a. Calculate the standard error of the mean.

_______

​(Round to four decimal places as​ needed.)

b. What is the probability that the sample mean will be less than ​$8.20​?

P(x<$8.20)=_____

​(Round to four decimal places as​ needed.)

c. What is the probability that the sample mean will be less than ​$7.98​?

P(x<$7.98)=_____

​(Round to four decimal places as​ needed.)

d. What is the probability that the sample mean will be more than ​$8.14​?

P(x>$8.14)=______

​(Round to four decimal places as​ needed.)

Answer 1

Since here sample size is greater than 30 which implies that we can assume that movies prices follows normal distribution.

So if denotes movie prices then

n = 40

So

A)

B)

C)

Similarly we can find

D)

where is the CDF of the standard normal distribution.

which is calculated in R

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