2. A new program implemented at the Houston College rewards outstanding teachers
ID: 3336113 • Letter: 2
Question
2. A new program implemented at the Houston College rewards outstanding teachers with the title "Distinguished Educator" and a $1,000 bonus. To receive this designation a teacher must rank in the 10% of faculty in schools that are members of the Colleges Committed to Excellence in Education. The teaching evaluation scores for all faculty in the CCEE consortium for this past year had an average of 73 with a standard deviation of 7.2. Additionally, these teaching evaluation scores will be used to identify and weed out very poor educators. The bottom 5% of teachers will be dismissed from their jobs. Answer the following questions based on this information. 1+1+3+3+3+3+1=12 What is the minimum percentile a teacher must have on the evaluation to qualify to be a Distinguished Educator? a) b) What is the maximum percentile a teacher can have and still be dismissed? c) What percentile is an evaluation score of 877 d) What percentile is an evaluation score of 71? e) What percentile is an evaluation score of 64? a. 90m percentile a. 5th percentile a. 97m percentileExplanation / Answer
Given
1.For being a distinguished education someone needs to rank within the top 10% people.
2.A teacher will be dismissed from its job if it comes in bottom 5%
3.Mean score in 73.Standard deviation is 7.2
Now,
There are 12 teachers,10% of this 12 teacher is (12*10/100)=1.2.i.e
Here the percentile of the marks=t,
t=73+Zm*(7.2/(square root of 12))
where Zm=upper (m/100) percent value of normal (0,1) distribution.
assuming marks follow normal distribution.putting different values of m we will get marks for different percentile.
a.we put m=10
b.we put m=95
c.here it is given t=marks, we need to find m. i.e m=Z inverse(t-73)*(square root (12))./7.2
Same goes for d and e
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