Please answer them all with step by step solutions The weekly income of a large
ID: 3134557 • Letter: P
Question
Please answer them all with step by step solutions
The weekly income of a large group of middle managers are normally distributed with the mean of $800 and a standard deviation of $45. what is the probability of finding a middle manager with a weekly income of between S840 and $900, what is the percentage of middle managers that earn more the $905 what is the percentage of middle managers that earn less than $905 what is the probability of finding a middle manager with weekly income of between $ 750 and $ 850 what is the probability of finding a middle manager with weekly income of between $ 750 and 790 above what income would the top 10% managers earn below what income would the lowest 10% of managers earnExplanation / Answer
a)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 840
x2 = upper bound = 900
u = mean = 800
s = standard deviation = 45
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = 0.888888889
z2 = upper z score = (x2 - u) / s = 2.222222222
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.812968601
P(z < z2) = 0.986865854
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.173897253 [ANSWER]
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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 = 905
u = mean = 800
s = standard deviation = 45
Thus,
z = (x - u) / s = 2.333333333
Thus, using a table/technology, the right tailed area of this is
P(z > 2.333333333 ) = 0.009815329 [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 = 905
u = mean = 800
s = standard deviation = 45
Thus,
z = (x - u) / s = 2.333333333
Thus, using a table/technology, the right tailed area of this is
P(z > 2.333333333 ) = 0.009815329 [ANSWER]
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d)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 750
x2 = upper bound = 850
u = mean = 800
s = standard deviation = 45
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1.111111111
z2 = upper z score = (x2 - u) / s = 1.111111111
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.133260263
P(z < z2) = 0.866739737
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.733479474 [ANSWER]
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