The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 215 milligrams per deciliter and a standard deviation of 38.8 milligrams per deciliter
(a) What percent of the men have a total cholesterol level less than 225 milligrams per deciliter of blood?
(b) If 241 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 257 milligrams per deciliter of blood
Solution :
Given that ,
mean =
= 215
standard deviation =
= 38.8
(a)
P(x < 225) = P[(x -
) /
< (225 - 215) / 38.8]
= P(z < 0.26)
= 0.6026
Probability = 0.6026
(b)
P(x > 257) = 1 - P(x < 257)
= 1 - P[(x -
) /
< (257 - 215) / 38.8]
= 1 - P(z < 1.08)
= 0.1401
Probability = 0.1401
241 * 0.1401 = 34 would you expect .
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