Show transcribed image text B. Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on t cell phone contract; the analyst finds that for those people who exceed the time included in their basic contract, the excess time used follows an exponenti distribution with a mean of 22 minutes. Consider a random sample of 80 customers who exceed the time allowance included in their basic cell phone contract Let x = the excess time used by one INDIVIDUAL cell phone customer who exceeds his contracted time allowance x Exp(1/22) This means the distribution of x is skewed right with μ 22 and σ 22 As is common practice, I would write an x with a bar on top to denote the mean of the sample, but I can't so I will write "x-bar" instead. So let x-bar the mean excess time used by a sample of n = 80 customers who exceed their contracted time allowance. Then by the central limit theorem for sample means x-bar is approximately normal, N(22, 22/sqrt80) Using the Central Limit Theorem to find probability Find the probability that the mean excess time used by the 80 customers in the sample is longer than 20 minutes. This is asking us to find P(xx> 20). Draw the graph. 1. 2. Suppose that one customer who exceeds the time limit for his cell phone contract is randomly selected. Find the probability that this individual customer's excess time is longer than 20 minutes.sis asking you to find P(x> 20). 3. Explain why the probabilities in parts a and b are different. Using the Central Limit Theorem to find percentiles. Find the 95th percentile for the sample mean excess time for samples of 80 customers who exceed their basic contract time allowances. Draw a graph.
B. Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on t cell phone contract; the analyst finds that for those people who exceed the time included in their basic contract, the excess time used follows an exponenti distribution with a mean of 22 minutes. Consider a random sample of 80 customers who exceed the time allowance included in their basic cell phone contract Let x = the excess time used by one INDIVIDUAL cell phone customer who exceeds his contracted time allowance x Exp(1/22) This means the distribution of x is skewed right with μ 22 and σ 22 As is common practice, I would write an x with a bar on top to denote the mean of the sample, but I can't so I will write "x-bar" instead. So let x-bar the mean excess time used by a sample of n = 80 customers who exceed their contracted time allowance. Then by the central limit theorem for sample means x-bar is approximately normal, N(22, 22/sqrt80) Using the Central Limit Theorem to find probability Find the probability that the mean excess time used by the 80 customers in the sample is longer than 20 minutes. This is asking us to find P(xx> 20). Draw the graph. 1. 2. Suppose that one customer who exceeds the time limit for his cell phone contract is randomly selected. Find the probability that this individual customer's excess time is longer than 20 minutes.sis asking you to find P(x> 20). 3. Explain why the probabilities in parts a and b are different. Using the Central Limit Theorem to find percentiles. Find the 95th percentile for the sample mean excess time for samples of 80 customers who exceed their basic contract time allowances. Draw a graph.
