The duration of a cellular telephone call is an

Chapter 9, Problem 9.34

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The duration of a cellular telephone call is an exponential random variable 'vith expected value 150 seconds. A subscriber has a calling plan that includes 300 minutes per month at a cost of $30.00 plus $0.40 for each minute that the total calling time exceeds 300 minutes. In a certain month, the subscriber has 120 cellular calls. (a) use the central limit theorem to estimate the probability that the subscriber's bill is greater than $36. (Assume that the durations of all phone calls are mutually independent and that the telephone company measures call duration exactly and charges accordingly, 'vithout rounding up fractional minutes.) (b) Suppose the telephone company does charge a full minute for each fractional minute used. Re-calculate your estimate of the probability that the bill is greater than $36.