Question

4.[5 marks] Suppose that Best Buy sells 4 TVs per day on average. a) [1 marks) What is the probability that 8 TVs will be sold in a day? b) [2 marks] What is the probability that fewer than 3 TVs (inclusive) will be sold in a day? c) [2 marks] Suppose 5 customers enter Best Buy independently. The probability that a single customer will buy a TV is 0.1. What is the probability that at least one of these 5 customers buys a TV? Do not round your answer.

Answer 1

(a)

Probability Mass Function of Poisson Distribution with mean = 4 is given by:

   for x = 0, 1, ...

So,

Answer is:

0.0298

(b)

P(X3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

So,
P(X3) = 0.4335

So,

Answer is:

0.4335

(c)

Binomial Distribution

n = 5

p = 0.1

q = 1 - p = 0.9

So,

P(X1) =1 - P(X=0) = 1 - qⁿ = 1 - 0.9⁵ = 1 - 0.59049 = 0.40951

So,

Answer is:

0.40951