1.It is known that in the absence of treatment,45% of the patients with a certain illness will improve. The Central Limit Theorem tells us that the percentages of patients in groups of 400 that improve in the absence of treatment are approximately normally distributed.

(a) Find the mean and standard deviation of the normal distribution given by the Central Limit Theorem. Round the standard deviation to one decimal place.

mean%

standard deviation%

(b) In what percentage of such groups (of 400) would175or fewer improve? Round your answer to one decimal place.

2.Suppose we toss 100 fair coins and record the percentage of heads.

According to the Central Limit Theorem, the percentages of heads resulting from such experiments are approximately normally distributed.

What is thez-score for58heads?

z=

How about62heads?

z=

3.A large jar is filled with marbles. Of these marbles,35% are red and the rest are blue. We randomly draw 100 marbles.

According to the Central Limit theorem, the percentages of red marbles in such samples are approximately normally distributed. Find the mean and standard deviation of this normal distribution. Round the standard deviation to one decimal place.

mean

standard deviation

4.About 35% of Americans over age 20 are obese.

(a) If we take random samples of400Americans over age 20 and record the percent of people in the sample who are obese, we expect to get data that are approximately normally distributed. Find the mean and standard deviation of this normal distribution. Round the standard deviation to one decimal place.

mean%

standard deviation%

(b) Would it be unusual to find a random sample of400Americans over 20 in which at least 38% were obese?

Yes, less than 5% of such samples would have at least 38% of the folks obese, so this would be unusual.

No, more than 5% of such samples would have at least 38% of the folks obese, so this would not be unusual.

5.A poll on a certain policy reports63% approval with a margin of error of5%. What is the confidence interval for this poll?

The confidence interval is from% (smaller value) to% (larger value).

6.A sample size of700people is used for a poll. What is the approximate margin of error for a 95% confidence interval? (Round your answer to one decimal place.)

Margin of error =%

7.What sample size is needed to give a margin of error of5% with a 95% confidence interval?

Sample size =