Say the heights of males in two different ethnic groups, A and B, are Normally d
ID: 3160073 • Letter: S
Question
Say the heights of males in two different ethnic groups, A and B, are Normally distributed, both with SD=10cm, but mean height in population A is 175cm and in population B it is 185cm. Relative to ethnic group B, the spread of heights for ethnic group A is w ider, narrower or the same? Why? The proportion of men in ethnic group B with height greater than 185cm is? The proprotion of men in ethnic group A with height greater than 185cm is? What proportion of men in ethnic group B will be taller than the average height in ethnic group A?Explanation / Answer
a)
The same, as they have the same standard deviation.
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 185
u = mean = 185
s = standard deviation = 10
Thus,
z = (x - u) / s = 0
Thus, using a table/technology, the right tailed area of this is
P(z > 0 ) = 0.5 [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 185
u = mean = 175
s = standard deviation = 10
Thus,
z = (x - u) / s = 1
Thus, using a table/technology, the right tailed area of this is
P(z > 1 ) = 0.158655254 [ANSWER]
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d)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 175
u = mean = 185
s = standard deviation = 10
Thus,
z = (x - u) / s = -1
Thus, using a table/technology, the right tailed area of this is
P(z > -1 ) = 0.841344746 [ANSWER]
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