Question

The average production cost for major movies is 61 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 7 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

What is the distribution of X?X ~ N(,)

What is the distribution of ¯x? ¯x ~ N(,)

For a single randomly selected movie, find the probability that this movie's production cost is between 56 and 58 million dollars.

For the group of 7 movies, find the probability that the average production cost is between 56 and 58 million dollars.

Answer 1

a) X ~ N(61 , 18)

b)

c)

                                        

                                         = P(-0.28 < Z < -0.17)

                                         = P(Z < -0.17) - P(Z < -0.28)

                                         = 0.4325 - 0.3897

                                         = 0.0428

d) n = 7

                                     

                                      = P(-0.73 < Z < -0.44)

                                      = P(Z < -0.44) - P(Z < -0.73)

                                      = 0.3300 - 0.2327

                                      = 0.0973