Question 5.91

61. One reason that normal distributions are important is that they describe how the results of an opinion poll would vary if the poll were repeated many times. About 40% of adult Americans say they are afraid to go out at night because of crime. Take many randomly chosen samples of 1050 people. The proportions of people in these samples who stay home for fear of crime will follow the normal distribution with a mean of 0.4 and a standard deviation of 0.015. Use this fact and the 68-95-99.7 rule to answer these questions.

  1. In many samples, what percentage of samples gives results above 0.4? Above 0.43?
  2. In a large number of samples, what interval contains the middle 95% of proportions of people who stay home because of crime?

61.

(a) Because of the symmetry of the normal curves, 50% give results above 0.4; because 0.43 is above give results above 0.43.

(b) , or 0.37 to 0.43

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