3. Assume that the heights of men are normally distributed, with a mean of 68.2

Question

3. Assume that the heights of men are normally distributed, with a mean of 68.2 inches and a standard deviation of 2.8 inches. We randomly select 64 men.

a) Describe the sampling distribution of the sample mean height for a random sample of 64 men. Explain why.

Conditions:

Shape:

Center:

Spread:

b) If 64 men are randomly selected, find the probability that they have a mean height greater than 69.2 inches.

Z-score: ____________ Table Value: ____________ Final Answer: ____________ Concluding Sentence:

c) If one man is randomly selected, what is the probability that he has a height greater than 69.2 inches?

Z-score: ____________ Table Value: ____________ Final Answer: ____________ Concluding Sentence:

Explanation / Answer

a)Using Central limit theorem the sampling distribution of sample mean is normal with mean of 68.2 inches and standard deviation 2.8/root over 64=0.35

b)For X=69.2, z=(69.2-68.2)/0.35=2.85

P(X>69.2)=P(z>2.85)=1-0.9978=0.0022

c)For X=69.2, z=(69.2-68.2)/2.8=0.35

Thus, P(X>69.2)=P(z>0.35)=1-P(z<0.35)=1-0.6368=0.3632

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