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1.The heights of adult men in America are normally distributed,with a mean of 69.3 inches and a standard deviation of 2.63 inches.The heights of adult women in America are also normallydistributed, but with a mean of 64.2 inches and a standarddeviation of 2.54 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to twodecimal places)?

z =

b) What percentage of men are SHORTER than 6 feet 3 inches? Roundto nearest tenth of a percent.

%

c) If a woman is 5 feet 11 inches tall, what is her z-score (to twodecimal places)?

z =

d) What percentage of women are TALLER than 5 feet 11 inches? Roundto nearest tenth of a percent.

%

2.A population of values has a normal distribution with?=32.1?=32.1 and ?=61.9?=61.9. You intend to draw a random sampleof size n=48n=48.

What is the mean of the distribution of sample means?
?¯x=?x¯=

What is the standard deviation of the distribution of samplemeans?
(Report answer accurate to 2 decimal places.)
?¯x=?x¯=

3. A population of values has a normal distribution with?=114.5?=114.5 and ?=47?=47. You intend to draw a random sample ofsize n=147n=147.

What is the mean of the distribution of sample means?
?¯x=?x¯=

4. What is the standard deviation of the distribution of samplemeans (i.e. the standard error)?
(Report answer accurate to 2 decimal places.)
?¯x=?x¯=

5. SAT scores are distributed with a mean of 1,500 and astandard deviation of 300. You are interested in estimating theaverage SAT score of first year students at your college. If youwould like to limit the margin of error of your 95% confidenceinterval to 25 points, how many students should you sample?