4 Suppose that the cholesterol level of women at ages 2029 i

4. Suppose that the cholesterol level of women at ages 20{29 is normally distributed with a mean level 185 (in

mg/dL) and standard deviation 36.5 (in mg/dL). Let X be the cholesterol level of a randomly selected women

at ages 20{29.

(a) (1 point) What is the distribution of X ?

(b) (2 points) What is the probability that the cholesterol level of the randomly selected woman is more

than 200?

Suppose 16 women are picked at random. Let X be the mean cholesterol level of them.

(c) (2 points) Determine the expected value, the standard deviation of the sample mean cholesterol level,

X , and its distribution.

(d) (2 points) Find the probability that the sample mean cholesterol level is more than 200.

Show work please!

Solution

mu=185 std dev = 36.5

a) X is normal as sample size is large we can approximate to normal

b) Std error = 36.5/4 = 9.125

P(X>200) = P(Z>15/9.125)

=P(Z>1.64) = 1-0.9495

= 0.0505

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c) Expected value = 185

std dev of sample mean = 36.5/rtn where n = sample size

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d) P(X bar>200) = 0.0505

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