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8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.

8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.
Transcribed Image Text:8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.
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