Question

The ticket sales for events held at the new civic center are believed to be normally distributed with a population mean of 12,000 tickets and a population standard deviation of 1,000 tickets.

a. What is the probability of selling less than 13,500 tickets?

b. What are the ticket sales for the top 15% of events held at the new civic center?

Answer 1

Solution :

Given that ,

mean = = 12000

standard deviation = = 1000

P(X<13500 ) = P[(X- ) / < (13500-12000) /1000 ]

= P(z < 1.5)

Using z table

= 0.9332

b

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.04 ) = 0.85

z =1.04

Using z-score formula,

x = z * +

x =1.04 * 1000+12000

x = 13040