Question

Suppose that 74% of all adults think that the overall safety of airline travel is either good or excellent. An opinion poll plans to ask an SRS of 1097 adults about airplane safety. The proportion of the sample who think that the overall safety of airline travel is either good or excellent will vary if we take many samples from this same population. The sampling distribution of the sample proportion is approximately Normal with mean 0.74 and standard deviation about 0.012. Sketch this Normal curve and use it to answer the following questions. (Round your answers to three decimal places.)

(a) What is the probability that the poll gets a sample in which more than 76.4% of the people think that the overall safety of airline travel is either good or excellent?

(b) What is the probability of getting a sample that misses the truth (74%) by 2.4% or more?

Answer 1

a)

population proportion ,p=   0.74                      
n=   1097                      
                          
std error , SE = 0.0120                      
                          
sample proportion , p̂ =   0.764                      
Z=( p̂ - p )/SE= (   0.764   -   0.74   ) /    0.0120   =   2.000
P ( p̂ >    0.764   ) =P(Z > ( p̂ - p )/SE) =                  
                          
=P(Z >   2.000   ) =    0.0228              

b)

P(p > 0.74+0.024 or p < 0.74-0.024) = P(p>0.764 or p <0.716) = 2 * P(p>0.764) = 2 * 0.0228= 0.0456