Question

1. Elly's Hotdog Emporium is famous for its chilidogs. Elly's latest sales indicate that 40% of customers order their chilidogs with hot peppers. Suppose 10 customers who have ordered their chilidogs are selected at random.

Required:

a. How many customers will ask for hot peppers in the expectation?    

b. What is the probability that exactly 7 customers will ask for hot peppers?

c. What is the probability that between two and six people inclusive want hot peppers?   

d. If Elly wants to repeat this experiment tomorrow, what is the probability that at least two customers will want hot peppers. Assume that the expected number of customers who want hot pepper is unchanged.                           

Answer 1

solution;

so let p be the probability that customer order their chilidog with hot pepper

so p = 40% = 0.4

n = 10

so X is Bino (10, 0.4)

a)

expected customer ask for hot pepper is = = E(X) = n*p = 10*0.4 = 4

b) probability that exactly 7 customer will ask for hot pepper = P(X =7)

formula for binomial probability =

so

c) probability that between 2 and 6 people inclusive want hot pepper=

= P(x=2) + P(X=3) + P(X= 4) + P(X=5) + P(X=6)

= 0.1115 + 0.2007 + 0.2508 + 0.215 + 0.1209 = 0.8989

d)

probability that atleast two customer want hot pepper = 1 - P(X=0) - P(X=1)

probability that atleast two customer want hot pepper = 1 - 0.006 - 0.0403 = 0.9537