Question

 

Tom works in a shop. On average, he sees that 3 purchasers come to the shop every hour. Calculate the following:

a) What is the probability that at least 2 and as many as 4 purchasers come to the shop in a given hour?

b) The mean rate of purchaser decreases to 5 purchasers every 2 hours. During one hour, what is the most likely number of purchasers that will come to the shop (hint: the answer must be an integer)?

Answer 1

a)

X= number of purchases in a given hour

X follows poisson distribution with mean = lambda = 3

P(2 <= X <= 4)

= P(X = 2) + P(X = 3) +P(X = 4)

= e^(-3) 3^2/2 + e^(-3) * 3^3/6 + e^(-3) 3^4/24

= 02240 + 02240 + 01680

= 0.6161

b)

mean = 5/2 = 2.5

we need to find the mode

mode is   2

Proof