5.71 Cyberbullying, continued. Refer to Exercise 5.69. Assume instead that that you sample n = 500 young people from the United Kingdom.

1. (a) What is the probability that the sample proportion of those who received nasty messages is between 0.59 and 0.65 if the population proportion is p = 0.62?

2. (b) What is the probability that the sample proportion is between 0.87 and 0.93 if the population proportion is p = 0.90?

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   (c) Using the results from parts (a) and (b), how does the probability that falls within ±0.03 of the true p change as p gets closer to 1?