The opera theater manager calculates that 14 of the opera ti

The opera theater manager calculates that 14% 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 819 tickets would be less than 12%? Round your answer to four decimal places.

Solution

Normal Distribution
Proportion ( P ) =0.14
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.14*0.86/819)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.12) = (0.12-0.14)/0.0121
= -0.02/0.0121= -1.6529
= P ( Z <-1.6529) From Standard Normal Table
= 0.0492