Question

The answers are in red! Thank you in advance

Assume the average price for a movie is $8.21. Assume the population standard deviation is $0.58 and that a sample of 34 theaters was randomly selected. Complete parts a through d below. a. Calculate the standard error of the mean. - = $ 0.0995 (Round to four decimal places as needed.) b. What is the probability that the sample mean will be less than $8.38? P(x < 58.38) = 0.9563 (Round to four decimal places as needed.) c. What is the probability that the sample mean will be less than $8.15? P(X<$8.15) = 0.2732 (Round to four decimal places as needed.) d. What is the probability that the sample mean will be more than $8.33? P(x> $8.33) = 0.1138 (Round to four decimal places as needed.)

Answer 1

u= 8.21
,
0 = 0.58
, $n=34$

a) Standard Error :

σε -

0.58 oT= = 0.0995 V34

b)

PT <8.38)

Z = 2

8.38 – 8.21 Z = 0.099951.7091

Plī <8.38) = P(Z < 1.7091) = 0.9563

#value of z is obtain from standard normal table

c)

Plī < 8.15)

Z = 2

= 8.15-8.21 0.09995 -=-0.6032 一

PI< 8.15) = P(Z < -0.6032) = 0.2732

d)

PT> 8.33)

Z = 2

Z = 8.33 - 8.21 0,09995 -= 1.2064

PT> 8.33) = P(Z > 1.2064) = 1- P(Z < 1.2064)

  

=1-0.8862 = 0.1138

PT> 8.33) = 0.1138