The average high school teacher salary is 43000 Let teacher

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?

Solution

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]