Question

Past data indicate that probability that troubles in residential service can be repaired on the same day is 0.6. For the 9 troubles reported on the same day what is the probability: a) at least 2 will be repaired on the same day? b) what are mean and standard deviation of this distribution?

Answer 1

Solution

Given that ,

p = 0.6

q = 1 - p = 1 - 0.6 = 0.4

n = 9

Using binomial probability formula ,

P(X = x) = (n C x) * p x * (1 - p)n - x

P(X 2 ) = 1 - P( x <2)

= 1 - P(X = 0) - P(X = 1)

= 1 - (9 C 0) * 0.6 0 * (0.4)9- (9 C 1) * 0.6 1 * (0.4)8

=1-0.0038

probability=0.9962

(B)

Using binomial distribution,

mean and standard deviation

Mean = = n * p = 9 *0.6 = 5.4

Mean =   =5.4

Standard deviation = = n * p * q = 9*0.6 * 04 = 1.4697

Standard deviation = = 1.4697