Question

At the entrance of Walmart, there is a greeter named Mary who says “Have a nice day” to the customers as they leave the store after shopping. The probability that a customer responds to Mary is 70%.

c) Mary just started her work shift at Walmart. She has said “have a nice day” to 3 people and received no response. What is the probability that it will take more than 5 people total for Mary to get her first response?

d) What is the probability that Mary will get her 4rd response, from the 7th person who walks out?

e) The store manager knows that after 5 pm, on average there are 20 customers leaving the store every 30 minutes. What is the probability that 5 customers leave Walmart between 6:10 and 6:20 pm?

Answer 1

c) probability that it will take more than 5 people total for Mary to get her first response

=P(X>5|X>=3)=P(X>2)=P(none of first 2 responds)=(1-0.7)² =0.09

d)

probability that Mary will get her 4rd response, from the 7th person who walks out =P(exactly 3 response from 1st 6 person and 4th response from 7th person)=⁶C₃(0.7)⁴(0.3)³ =0.129654

e)

expected number of customer leaving in 10 minutes(between 6:10 and 6:20)=20*10/30=6.67

hence P( 5 customers leave Walmart between 6:10 and 6:20 pm )=e^-6.67*6.67⁵/5! =0.139542