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.

a. Calculate the standard error of the proportion=0.0364 ​(Round to four decimal places as​ needed.)

b. What is the probability that less than 81 of them are​ first-time buyers?​P(Less than 81 of them are​ first-time ​buyers)=______ ​(Round to four decimal places as​ needed.)

c. What is the probability that more than 89 of them are​ first-time buyers? ​P(More than 89 of them are​ first-time ​buyers)_______​(Round to four decimal places as​ needed.)

**I get as far as solving the problem, but I don't think I'm looking up the Z score correctly. For example,part b above, I get z<0.2307, look it up on the table and I get 0.5910. What am I doing wrong? Can someone explain it to me.

Answer 1

The proportion of homes purchased by first-time buyers is

a) The standard error of proportion is

b) We can assume the proportion has normal distribution with mean and standard deviation .

The z-score corresponding to is

  is

The probability,

Look up the cumulative standard normal distribution table corresponding to 0.2153.

c)The probability,