The Centers for Disease Control and Prevention reported that diastolic blood pre
ID: 3135065 • Letter: T
Question
The Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.5 millimeters of Mercury and standard deviation 9.9 mm Hg.
a.
b.
c.
Find the proportion of adult women who have diastolic blood pressure of more than 78 mm Hg.
Find the diastolic blood pressure range for the middle 70% of adult women.
25% of adult women have a diastolic blood pressure above what amount?
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Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 78
u = mean = 80.5
s = standard deviation = 9.9
Thus,
z = (x - u) / s = -0.252525253
Thus, using a table/technology, the right tailed area of this is
P(z > -0.252525253 ) = 0.599682451 [ANSWER]
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b)
As the middle area is
Middle Area = P(x1<x<x2) = 0.7
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.15
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -1.036433389
By symmetry,
z2 = 1.036433389
As
u = mean = 80.5
s = standard deviation = 9.9
Then
x1 = u + z1*s = 70.23930944
x2 = u + z2*s = 90.76069056
Hence, between 70.23930944 and 90.76069056. [ANSWER]
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c)
First, we get the z score from the given left tailed area. As
Left tailed area = 1 - 0.25 = 0.75
Then, using table or technology,
z = 0.67448975
As x = u + z * s,
where
u = mean = 80.5
z = the critical z score = 0.67448975
s = standard deviation = 9.9
Then
x = critical value = 87.17744853 [ANSWER]