Question

Please include bell shape curve.

According to the National Association of Realtors, 44% of U.S. homes sold in March 2010 were purchased by first-time buyers. A random sample of 175 people who just purchased homes is selected.

a. Calculate the standard error of the proportion.

b. What is the probability that less than 80 of them are first-time buyers?

c. What is the probability that more than 84 of them are first-time buyers?

d. What is the probability that between 66 and 72 of them are first-time buyers?

Answer 1

Given that the population proportion is 0.44 and sample size is 175, so by using Z score we find Probability,

a) Standard error of proportion is calculated as

b) Now if sample proportion to be less than

So,

now,

The desired probability is calculated using Z table shown below:

=0.6772

Bell curve numerating Z

c) at X=84

so,

So,

=0.4562

d) the probability that between 66 and 72 of them are first-time buyers

Z at X= 66

Z as

now

at X=72

Z at X=72

So, probability as

Using Z table shown below

=0.5160-0.0465

=0.4695