Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places.

Part a)

What is the probability that exactly two customers arrive in a minute?

Part b)

Find the probability that more than three customers arrive in a two-minute period.

Part c)

What is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?

question c is not 0.442

Solutions

Expert Solution

Let X denotes the number of customers arrive at a grocery store in a minute.

X ~ Poisson(2.1)

The probability mass function of X is

a) The probability that exactly two customers arrive in a minute is

b) Let Y denotes the number of customers arrive at a grocery store in a 2 minute period.

Y ~ Poisson(2.1*2) or Y ~ Poisson(4.2)

The probability mass function of Y is

The probability that more than three customers arrive in a two-minute period is

c) The probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute is

= P( at least 5 customers arrive in two minutes)

milcah answered 2 months ago

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