3. A store opens at 8 A.M. and closes at 6 P.M. From 8 until 10 customers arrive at a Poisson rate of 5 an hour. Between 10 and 12 they arrive at a Poisson rate of 9 an hour. From 12 to 2 the arrival rate increases steadily from 9 per hour at 12 to 15 per hour at 2; and from 2 to 6 the arrival rate drops steadily from 15 per hour at 2 to 7 per hour at 6. (a) What is the expected number of customers that enter the store on a given day? (b) What is the probability that from 12 to 2, there are exactly 20 customers arrive? Compute this number numerically.

A First Course in Probability (10th Edition)
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3. A store opens at 8 A.M. and closes at 6 P.M. From 8 until 10 customers arrive at a Poisson
rate of 5 an hour. Between 10 and 12 they arrive at a Poisson rate of 9 an hour. From 12
to 2 the arrival rate increases steadily from 9 per hour at 12 to 15 per hour at 2; and from
2 to 6 the arrival rate drops steadily from 15 per hour at 2 to 7 per hour at 6.
(a) What is the expected number of customers that enter the store on a given day?
(b) What is the probability that from 12 to 2, there are exactly 20 customers arrive?
Compute this number numerically.
Transcribed Image Text:3. A store opens at 8 A.M. and closes at 6 P.M. From 8 until 10 customers arrive at a Poisson rate of 5 an hour. Between 10 and 12 they arrive at a Poisson rate of 9 an hour. From 12 to 2 the arrival rate increases steadily from 9 per hour at 12 to 15 per hour at 2; and from 2 to 6 the arrival rate drops steadily from 15 per hour at 2 to 7 per hour at 6. (a) What is the expected number of customers that enter the store on a given day? (b) What is the probability that from 12 to 2, there are exactly 20 customers arrive? Compute this number numerically.
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