Question

A group of realtors estimates that​ 23% of all homes purchased last year were considered investment properties. If a sample of 800 homes sold last year is​ obtained, what is the probability that at least 175 homes are going to be used as investment​ property? Round to four decimal places.

Answer 1

Answer:

Probability = 0.77488

Step-by-step explanation:

Since a sample was obtained, this problem is working with the sampling distribution of the sample proportion (p').l which we will need to find the probability.

A sampling distribution of the sample proportion has a mean equal to the population proportion (p).

The standard deviation of the distribution is equal to √((p(1-p))/n).

The sampling distribution in this problem will be normal because the sample size is large.

For this question, the sample proportion(p) is; 23% = 0.23

The sample size(n) is 800, so the standard deviation is;

SD = √((p(1-p))/n) = √((0.23(1-0.23))/800)

SD = 0.0149

The sample proportion is;

(p') = 175/800

p' = 0.21875

Now, for the Z-score;

z = (p' - mean)/SD

z = (0.21875 - 0.23)/ 0.0149

z = - 0.755

Now for the probability, since at least 175,it will be right tail. Thus from the table i attached;

P(z > -0.755) = 1 - 0.22663 = 0.77488