A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard of 20.
-A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20.What is the number of patrons,x,where 80% are less than x?
A)216.8
B)597.2
C)413.3
D)297.2
E)332.8

Question

Quizplus · Accepted Answer

To find the number of patrons, x, where 80% are less than x, we need to find the z-score that corresponds to the 80th percentile.

Using a standard normal distribution table, we can find that the z-score for the 80th percentile is approximately 0.84.

We can then use the formula:

z = (x - μ) / σ

where z is the z-score, μ is the mean, and σ is the standard deviation.

Plugging in the values we know:

0.84 = (x - 200) / 20

Solving for x:

x - 200 = 0.84 * 20

x - 200 = 16.8

x = 216.8

Therefore, the answer is A) 216.8.

A Plant Manager Knows That the Number of Boxes of Supplies