Answer to Question #141966 in Statistics and Probability for Lamak

Question

An important part of the customer services responsibilities of a telephone company relates to the speed with which reported troubles in residential services can be repaired. Suppose that past data indicate that 70% of the reported troubles in residential services can be repaired on the same day. If 100 troubles are reported on a given day, calculate the probability that at most 80 will be repaired on the same day.

Answer 1

This is a binomial distribution with $p=0.7,\;n=100$.

It can be approximated by the normal distribution with

$\mu=np=100*07=70,$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.7*0.3}=4.58.$

Thus, $P(X\le80)=P(Z<\frac{80.5-70}{4.58})=P(Z<2.29)=0.9890.$