Question

(15 pts total) In 2013, the average length of a feature length film was 86 minutes with a standard deviation of 24 minutes. Source: IMDB.com/interfaces

a) (2 pts) Explain why it is inappropriate to use the normal model to find the probability that a random sample of 15 films will have a mean length greater than 115 minutes.

b) (5 pts) Describe the sampling distribution of x for n = 40 films (Shape, Center, Spread, with justification).

c) (3 pts) Using the Standard Normal Table, find the proportion of samples of size n = 40 that will have a mean length greater than 115 minutes.

d) (2 pts) Will the proportion found in c) be greater than or less than the proportion of samples of size n = 65 that will have a mean length greater than 115 min? Explain. e) (3 pts) There is a 4% probability that a random sample of 40 films will have a mean length greater than ______. (Use the Standard Normal Table.)

Answer 1

SolutionA:

According to central limit theorem ,if a sample has size greater than or equal to 30 only follows normal distribution.

here sample size n=20

n<30

given sample is small sample.

does not follow normal distribution

Solution-B:

) Describe the sampling distribution of x for n = 40 films (Shape, Center, Spread, with justification).

n=40

large sample follow normal distribution with

shape=symmetircal

center=sample mean =xbar=mu=86

spread=sample stddev=s=sigma/sqrt(n)=24/sqrt(40)=3.794733