Suppose that a phone company reports that the average duration of a cell phone call is 1.7 minutes, with a standard deviation of 1.4 minutes.
- Would it be reasonable to use a normal distribution to model the duration of cell phone calls? Explain
- Suppose you want to examine a random sample of 60 cell phone calls. Do you think it would be reasonable to use the Central Limit Theorem to describe the sampling distribution of the sample mean call duration? Explain.
- What does the CLT say about the sampling distribution of the sample mean call duration in a random sample of 60 calls?
- Draw a well-labeled sketch to accompany your answer to question 3.
- Describe how the sketch would change if the sample size were 160 calls rather than 60 calls.
Suppose 80% of the incoming email messages for a college’s computer system are spam
- Use the CLT to approximate the probability that in a random sample of 200 incoming email messages at this college, the sample proportion of these messages that are spam would exceed .75
- Display your answer to previous question as a shaded area in a well-labeled sketch.
- After implements a new spam blocker, if it turns out that a random sample of 200 messages contains 75% spam, would this constitute fairly convincing evidence that the (population) percentage of spam has been reduced from 80%? Explain.
- Would your answer to question be larger, smaller, or the same if the sample size were 100 messages rather than 200 messages?
- Would your answer to question 1 be larger, smaller, or the same if the (population) proportion of spam messages were .77 rather than .80? Explain.