Solve the following:
Q1. Let X have a Poisson distribution with a mean of 4. Find
(a) P(2 ≤X≤5).
(b) P(X ≥3).
(c) P(X≤ 3).
Q2. Let X have a Poisson distribution with a variance of 3. Find P(X = 2).
Q3. Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poisson distribution. Give the probability that more than 10 customers arrive in a given hour.
Q4. If X has a Poisson distribution such that
3P(X = I) P(X is 2), find P(X = 4).
Q5. Flaws in a certain type of drapery material appear on the average of one in 150 square feet. If we assume a Poissondistribution, find the probability of at most one flaw appearing in 225 square feet 246. A certain type of aluminum screen that is 2 fee wide has, on the average, one flaw in a 100-foo roll. Find the probability that a 50400t roll ha: no flaws.
Q6. With probability 0.001, a prize of 5499 is woo it the Michigan Daily Lottery when a 81 straight be is plated. Let Y equal the number of 5499 prize won by a gambler after placing n straight bets Note that Y isb(n,0.001 ). After placingn mg 200t 51 bets, the gambler is behind if {Y 5 4}. Use. the Poisson distribution to approximate P(Y s 4 when n = 2000.
Q7. Suppose that the probability of suffering a sick effect from a certain flu vaccine is 0.005. If 1001 persons are inoculated, find the approximate probability that
(a) At most I person suffers.
(b) 4, 5. or 6 persons suffer.