A realtor has been told that 47% of homeowners in a city prefer to have a finished basement.She surveys a group of 400 homeowners randomly chosen from her client list.Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.
A)Binom(400,47%)
B)N(53%,2.5%)
C)N(47%,1.2%)
D)N(47%,2.5%)
E)There is not enough information to describe the distribution.

Question

Quizplus · Accepted Answer

The sampling distribution of the proportion of homeowners who prefer a finished basement in this sample follows a normal distribution with mean equal to the population proportion (47%) and standard deviation equal to the standard error of the proportion, which is calculated as the square root of [(0.47)(0.53)/400], resulting in a standard deviation of approximately 0.025 or 2.5%. Therefore, the correct choice is D.

A Realtor Has Been Told That 47% of Homeowners in a City