Let X be normally distributed with mean = 140 and standard deviation = 28. Use T
ID: 3129615 • Letter: L
Question
Let X be normally distributed with mean = 140 and standard deviation = 28. Use Table 1. a.
1. Find P(X 100)
2. Find P(95 X 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
3.
Find x such that P(X x) = 0.063. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)
4. Find x such that P(X > x) = 0.352. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)
Find x such that P(X x) = 0.063. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)
4. Find x such that P(X > x) = 0.352. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)
Explanation / Answer
1.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 100
u = mean = 140
s = standard deviation = 28
Thus,
z = (x - u) / s = -1.43
Thus, using a table/technology, the left tailed area of this is
P(z < -1.43 ) = 0.0764 [ANSWER]
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2.
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 95
x2 = upper bound = 110
u = mean = 140
s = standard deviation = 28
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1.61
z2 = upper z score = (x2 - u) / s = -1.07
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.0537
P(z < z2) = 0.1423
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.0886 [ANSWER]
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3.
First, we get the z score from the given left tailed area. As
Left tailed area = 0.063
Then, using table or technology,
z = -1.53
As x = u + z * s,
where
u = mean = 140
z = the critical z score = -1.53
s = standard deviation = 28
Then
x = critical value = 97.16 [ANSWER]
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4.
First, we get the z score from the given left tailed area. As
Left tailed area = 1-0.352 = 0.648
Then, using table or technology,
z = 0.38
As x = u + z * s,
where
u = mean = 140
z = the critical z score = 0.38
s = standard deviation = 28
Then
x = critical value = 150.64 [ANSWER]
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