Question

The opera theater manager calculates that 11% 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 703 tickets would be less than 13%? Round your answer to four decimal places.

Answer 1

Solution:

Given that,

n = 110

= 0.11

1 - = 1 - 0.11 = 0.89

So,

a ) =   = 0.11

=   ( 1 - ) / n

=   0.11 * 0.89 / 703

= 0.0118

= 0.0118

Standard error = 0.0474

p (   < 0.13 )

p ( -    / ) < ( 0.13 - 0.11 / 0.0118 )

p ( z < 0.02 / 0.0118 )

Using z table

p ( z < 1.69 )

= 0.9545

Probability = 0.9545