18.21 Airplane safety. Suppose that 73% 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 0.73 and standard deviation about 0.013. Sketch this Normal curve and use it to answer the following questions.
(a) What is the probability that the poll gets a sample in which more than 75.6% of the people think that airplanes would be safer if passengers were banned from carrying on board any luggage, including purses, computers, and briefcases?
(b) What is the probability of getting a sample that misses the truth (73%) by 2.6% or more?