Question

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day?a. 0.6328b. 0.0010c. 0.0156d. 0.0146

Answer 1

0.0156

Explanation:

Given X~Binomial (n=5, p=0.75)

x= number of trials

P(X=x)=xC_5×(0.75^x)×(0.25^(5-x))

So the probability is

P(X<2)=P(X=0)+P(X=1)

=0C_5×(0.75^0)×(0.25^(5-0))+1C_5×(0.75^1)×(0.25^(5-1))

=0.015625

Answer:0.0156