Question

In a neighborhood of 95 homes, 35 have pets. Suppose that 12 homes are selected at random. The random variable X represents the number of homes in the sample that have pets. Show your work.

(b) What is the probability of obtaining 8 homes with a pet?

(c) What is the probability of obtaining 9 homes with a pet?

(d) What is the probability of obtaining 12 homes with a pet? Would it be unusual to select 12 homes that have a pet?

(e) What is the mean and standard deviation of the random variable X?

Answer 1

X ~ B ( n = 12 , P = 0.36842 )

part b)

part c)

Part d)

Yes, it is unusual, because the probability is less than 0.05.

part e)

Mean = n * P = ( 12 * 0.36842 ) = 4.4211

Variance = n * P * Q = ( 12 * 0.36842 * 0.63158 ) = 2.7922

Standard deviation = √(variance) = (2.7922) = 1.671