Question

According to the​ research, 43 ​% of homes sold in a certain month and year were purchased by​ first-time buyers. A random sample of 185 people who just purchased homes is selected. Complete parts a through e below. a. Calculate the standard error of the proportion. =0.0364 ​(Round to four decimal places as​ needed.)

What is the probability that more than 78 of them are​ first-time buyers? ​P(More than 78 of them are​ first-time ​buyers)______ ​(Round to four decimal places as​ needed.)

Answer 1

GIVEN:

Proportion of of homes sold in a certain month and year were purchased by​ first-time buyers

Sample size of people who just purchased homes

(a) STANDARD ERROR OF PROPORTION:

The formula for standard error of proportion is given by,

Thus the standard error of proportion is,

Thus the standard error of proportion is .

PROBABILITY THAT MORE THAN 78 OF THEM ARE FIRST TIME BUYERS:

The sample proportion is given by,

  

In other words, the probability that more than 42% of the sample are first time buyers is .

To calculate the probability, we convert the sample proportion into standard score Z using the given formula,

Now the probability that more than 42% of the sample are first time buyers is,

{Since }

From the z table, the probability value is the value with corresponding row 0.2 and column 0.07.)

Thus the probability that more than 42% of the sample are first time buyers is . In other words, the probability that more than 78 of them are​ first-time buyers is .