Question

Question 22  Applying to College

You ask an SRS of 1500 college students whether they applied for admission to any other college.Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. (That’s close to the truth.) The sampling distribution of the proportion of your sample who say “Yes” is approximately Normal with mean 0.35 and standard deviation 0.01.

Choose the best answer for each problem below. Answers may be use once, more than once or not at all.

	What percentage of many samples would have a sample proportion less than .335? Use z-score (standard score) to find this answer.
	What percentage of many samples would have a sample proportion larger than 0.37? (Use the 68–95–99.7 rule.)
	What is the probability that your sample will have a proportion less than 0.33?
	Use Rule D: what is the probability that your sample result will be either less than 0.33 or greater than 0.37?

A.	5%
B.	10%
C.	6.68%
D.	1%
E.	2.5%
F.	-1.5

Answer 1

1()\

percentage of many samples would have a sample proportion less than .335 :

probability =P(X<0.335)=(Z<(0.335-0.35)/0.01)=P(Z<-1.5)=0.0668~ 6.68%

2)

percentage of many samples would have a sample proportion larger than 0.37 :

probability =P(X>0.37)=P(Z>(0.37-0.35)/0.01)=P(Z>2)=1-P(Z<2)=1-0.975=0.025 ~ 2.5 %

3) probability that your sample will have a proportion less than 0.33

probability =P(X<0.33)=(Z<(0.33-0.35)/0.01)=P(Z<-2)=0.0228 ~ 2.5 %

4) probability that your sample result will be either less than 0.33 or greater than 0.37

probability =1-P(0.33<X<0.37)=1-P((0.33-0.35)/0.01)<Z<(0.37-0.35)/0.01)=1-P(-2<Z<2)=0.05 ~ 5%