Question 1134344: 7. Consider the approximately normal population of heights of male college students with mean μ = 65 inches and standard deviation of σ = 4 inches. A random sample of 16 heights is obtained.
(a) Describe the distribution of x, height of male college students. (Choose one)
-skewed right
-approximately normal
-skewed left
-chi-square
(b) Find the proportion of male college students whose height is greater than 72 inches. (Give your answer correct to four decimal places.)
(c) Describe the distribution of x, the mean of samples of size 16.
-skewed right
-approximately normal
-skewed left
-chi-square
(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)
(ii) Find the standard error of the x distribution. (Give your answer correct to four decimal places.)
(e) Find P(x > 71). (Give your answer correct to four decimal places.)
(f) Find P(x < 70). (Give your answer correct to four decimal places.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the distribution is given as approximately normal. If the population is approximately normal, the sample mean is also from an approximately normal distribution and may be treated that way.
z=(x-mean)/sigma=(72-65)/4=1.75
probability of z>1.75 is 0.0401
The mean of the sampling distribution is also 65 in.
The SE is sigma/sqrt(n)=4/sqrt(16)=1 in
P(x>71): z>=(xbar-mu)/sigma/sqrt(n)
z>6/4/sqrt(16)=6. That probability is 0.
P(x<70) is z<(5*sqrt(16)/16=5. That probability is essentially 1 (0.9999)
It is quite possible for a single observation to be 7 inches away from the mean, but a mean of 16 of them will be far closer to the given sample mean
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