Question

Question In a large population, about 45% of newly constructed single-family homes have more than three bedrooms. A researcher takes a random sample of 15 homes and surveys whether they have more than three bedrooms. Use the binomial distribution to compute the probability that exactly 6 of the homes in the sample have more than three bedrooms. Identify the following information required to find the probability of new homes with more than three bedrooms. Provide your answer below:

n = trials

x = successes

p = probability of more than three bedrooms ACK

Answer 1

Here n = no. of samples of homes=15

Here X: no. of homes having more than three bedrooms in sample of 15 homes.

We have given that 45% of newly constructed single-family homes have more than three bedrooms.

Thus p=0.45

q= 0.55

We have to find, probability that exactly 6 of the homes in the sample have more than three bedrooms,that is P(X=6).

P(X=6)=BINOMDIST(6,15,0.45,0)

P(X=6)=0.191400633

Thus probability that exactly 6 of the homes in the sample of 15 have more than three bedrooms is 0.191400633