Answer to Question #113703 in Statistics and Probability for Katenda

Question

Suppose that the number of daily FKP is Poisson distributed with the mean of
0.2 posts per day. Use this information to answer questions 8, 9 and 10.

Question 8

What is the probability that on any given day there will be no FKP?
(1) 0.7408
(2) 0.2000
(3) 0.0000
(4) e^0.2
(5) None of the above

Question 9

Which one of the following statements is incorrect?
(1) The probability that there will be one FKP on any given day is 0.1637
(2) The probability that there will be two FKP on any given day is 0.0164
(3) The probability that there will be at least three FKP on any given day is 0.0012
(4) The probability that there will be at least five FKP on any given day is 0.0000
(5) None of the above.

Question 10

What is the value of the mean and the standard deviation of the number of daily FKP?
(1) µ = 0.2 and σ = 0.4
(2) µ = 0.2 and σ = 0.04
(3) µ = 0.2 and σ = 0.2
(4) µ = 0.4 and σ = 0.4
(5) µ = 0.4 and σ = 0.2

Answer 1

$p(x)=\frac {e^{-0.2}(0.2)^x}{x!} ,x=0,1,2,...\\ questions\; 8\\ p(x=0)=\frac {e^{-0.2}(0.2)^0}{0!} =0.8187\\ \text {The answer is (5) none of the above}\\ questions\; 9\\ (1)p(x=1)=\frac {e^{-0.2}(0.2)^1}{1!} =0.1637\\ (2)p(x=2)=\frac {e^{-0.2}(0.2)^2}{2!} =0.0164\\ (3)p(x\geq 3)=1-p(x\leq 2)\\ =1-[p(0)+p(1)+p(2)] =0.0012\\ (4)p(x\geq 5)=1-p(x\leq 4)\\ =1-[p(0)+p(1)+p(2)+p(3)+p(4)] \approx 0.0000\\ \text {The answer is (5) none of the above}\\ question 10\\ \text {The answer is (3) } \mu=0.2, \sigma ^2=0.2\\$