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
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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