Question

The opera theater manager calculates that 32% of the opera tickets for tonight's show have been sold.

If the manager is correct, what is the probability that the proportion of tickets sold in a sample of 719 tickets would differ from the population proportion by greater than 3%? Round your answer to four decimal place

Answer 1

Solution

Given that,

p = 0.32

1 - p = 1 - 0.32 = 0.68

n = 719

= p = 0.32

=  [p ( 1 - p ) / n] = [(0.32 * 0.68) / 719] = 0.0174

0.32 ± 0.03

=P ( 0.29 < < 0.35)

= 1 - P[(0.29 - 0.32) / 0.0174 < ( - ) / < (0.35 - 0.32) / 0.0174]

= 1 - P(-1.72 < z < 1.72)

=1 - P(z < 1.72) - P(z < -1.72)

Using z table,   

= 1 - ( 0.9573 - 0.0427 )

= 1 - 0.9146

= 0.0854