Use the information in Example 7.8, but use a sample size of 55 to answer the following questions. Quiz

PDF page 420: Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on their basic 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 exponential 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. ⎛ 1 ⎞ X ∼ Exp

PDF page 420: Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on their basic 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 exponential 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. ⎛ 1 ⎞ X ∼ Exp

PDF page 420: . From previous chapters, we know that μ = 22 and σ = 22.

PDF page 420: . From previous chapters, we know that μ = 22 and σ = 22.

PDF page 420: Suppose that a market research analyst for a cell phone company conducts a study of their customers who exceed the time allowance included on their basic 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 exponential 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. ⎛ 1 ⎞ X ∼ Exp

PDF page 420: ⎝22⎠ ̄ Let X = the mean excess time used by a sample of n = 80 customers who exceed their contracted time allowance. ̄ ⎛ 22 ⎞ by the central limit theorem for sample means X ~ N 22, ⎝ 80⎠ Using the clt to find probability

PDF page 420: ⎝22⎠ ̄ Let X = the mean excess time used by a sample of n = 80 customers who exceed their contracted time allowance. ̄ ⎛ 22 ⎞ by the central limit theorem for sample means X ~ N 22, ⎝ 80⎠ Using the clt to find probability

PDF page 420: a. Find the probability that the mean excess time used by the 80 customers in the sample is longer than 20

PDF page 420: ⎛ ̄ 22 ⎞ P( x > 20) = 0.79199 using normalcdf 20,1E99,22, ⎝ 80⎠ The probability is 0.7919 that the mean excess time used is more than 20 minutes, for a sample of 80 customers who exceed their contracted time allowance.

PDF page 420: ⎛ ̄ 22 ⎞ P( x > 20) = 0.79199 using normalcdf 20,1E99,22, ⎝ 80⎠ The probability is 0.7919 that the mean excess time used is more than 20 minutes, for a sample of 80 customers who exceed their contracted time allowance.

PDF page 421: P(x > 20) = e or e = 0.4029 ̄

PDF page 421: c. 1. P(x > 20) = 0.4029 but P( x > 20) = 0.7919

PDF page 421: b. Find P(x > 20). Remember to use the exponential distribution for an individual: X ~Exp

PDF page 421: variable; do not use the clt. Use the clt with the normal distribution when you are being asked to find the probability for a mean.

PDF page 421: variable; do not use the clt. Use the clt with the normal distribution when you are being asked to find the probability for a mean.

PDF page 421: Using the clt to find percentiles Find the 95 percentile for the sample mean excess time for samples of 80 customers who exceed their basic contract time allowances. Draw a graph.