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Airplane safety. Suppose that 68% of all adults think that airplanes would be safer places if airline passengers were banned from carrying on board any luggage, including purses, computers, and briefcases. An opinion poll plans to ask an SRS of 1023 adults about airplane safety. The proportion of the sample who think that airplanes would be safer if passengers were banned from carrying on board any luggage, including purses, computers, and briefcases, will vary if we take many samples from this same population. The sampling distribution of the sample proportion is approximately Normal with mean 0.68 and standard deviation about 0.015. 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 71% 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 (68%) by 3.0% or more?

 
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