Question

A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)? Assume the distribution is approximately normal.

Question 5 options:

1)

413.09

2)

163.03

3)	We do not have enough information to calculate the value.

4)

135.81

5)

114.25

Answer 1

Solution :

Given that,  

mean = = $138.64

standard deviation = = $11.2526

Using standard normal table,

P(Z > z) = 98.49%%

1 - P(Z < z) = 0.9849

P(Z < z) = 1 - 0.9849

P(Z < -2.167) = 0.0151

z = -2.167

Using z-score formula,

x = z * +

x = -2.167 * 11.2526 + 138.64 = 114.25

98.49% of movies grossed greater than how much money (in millions) = 114.25

option 5) is correct