Question

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 192 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.29?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = (Enter your answer as a number accurate to 4 decimal places.)

Answer 1

population proportion ,p=   0.34                          
n=   192                          
                              
std error , SE = √( p(1-p)/n ) =    0.034                          
                              
sample proportion , p̂ =   0.29                          
Z=( p̂ - p )/SE= (   0.290   -   0.34   ) /    0.034   =   -1.463  
P ( p̂ <    0.290   ) =P(Z<( p̂ - p )/SE) =                      
                              
=P(Z <    -1.463   ) =    0.0718                   (answer)

excel formula for probability from z score is =NORMSDIST(Z)