The average high school teacher salary is $43,000. Let teacher salary be normall
ID: 3396483 • Letter: T
Question
The average high school teacher salary is $43,000. Let teacher salary be normally distributed with a standard deviation of $18,000.
a) Mr.Lucky had been a teacher for only 2 years. Despite being new as a teacher, his salary is already in the top 5% of all high school salaries. Mr. Lucky must be making at least how much in salary?
b) Mr. Unucky has been a teacher for over 10 years, but his salary is in the bottom 20% of all high school salaries. Mr. Unlucky must be making at most how much in salary?
c) What percent of high school teachers make more than $80,000?
Explanation / Answer
a)
First, we get the z score from the given left tailed area. As
Left tailed area = 0.95
Then, using table or technology,
z = 1.644853627
As x = u + z * s,
where
u = mean = 43000
z = the critical z score = 1.644853627
s = standard deviation = 18000
Then
x = critical value = 72607.36529 [ANSWER]
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b)
First, we get the z score from the given left tailed area. As
Left tailed area = 0.2
Then, using table or technology,
z = -0.841621234
As x = u + z * s,
where
u = mean = 43000
z = the critical z score = -0.841621234
s = standard deviation = 18000
Then
x = critical value = 27850.8178 [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 = 80000
u = mean = 43000
s = standard deviation = 18000
Thus,
z = (x - u) / s = 2.055555556
Thus, using a table/technology, the right tailed area of this is
P(z > 2.055555556 ) = 0.019912688 = 1.991% [ANSWER]
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