Question

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

a.	What is the probability of selling more than 10,000 tickets?
b.	What is the probability of selling between 9,500 and 11,000 tickets?
c.	What is the probability of selling more than 13,500 tickets?

Answer 1

Solution :

a.

P(x > 10000) = 1 - P(x < 10000)

= 1 - P[(x - ) / < (10000 - 12000) / 1000)

= 1 - P(z < -2)

= 1 - 0.0228

= 0.9772

probability = 0.9772

b.

P(9500 < x < 11000) = P[(9500 - 12000)/ 1000) < (x - ) /  < (11000 - 12000) / 1000) ]

= P(-2.5 < z < -1)

= P(z < -1) - P(z < -2.5)

= 0.1587 - 0.0062

= 0.1525

probability = 0.1525

c.

P(x > 13500) = 1 - P(x < 13500)

= 1 - P[(x - ) / < (13500 - 12000) / 1000)

= 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

probability = 0.0668