Akron Cinema sells an average of 500 tickets on Mondays, with a standard deviation of 50 tickets. If a simple random sample is taken of the mean amount of ticket sales from 30 Mondays in a year, what is the probability that the mean will be greater than 510?

Step-by-step explanation:

Assuming the number of tickets sales from Mondays is normally distributed. the formula for normal distribution would be applied. It is expressed as

z = (x - u) / s

Where

x = ticket sales from monday

u = mean amount of ticket

s = standard deviation

From the information given,

u = 500 tickets

s = 50 tickets

We want to find the probability that the mean will be greater than 510. It is expressed as

P (x greater than 510) = 1 - P (x lesser than or equal to 510)

For x = 510

z = (510 - 500) / 50 = 0.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.9773

P (x greater than 510) = 1 - 0.9773 = 0.0227

the correct answer is 0.1366