In order to help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 122.6, find the cutoff score that will make a student eligible for the program. The standard deviation is 18. Assume the variable is normally distributed. Round to two decimal places.

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Answer:

92.99

Step-by-step explanation:

Mean, μ = 122.6

Standard deviation, σ = 18

Recall :

Z = (x - μ) / σ

x = score

The Zscore for the lower 5% = 0.05

Using, invnorm(0.05) = - 1.645

Put Z = - 1.645

-1.645 = (x - 122.6) / 18

-1.645 * 18 = x - 122.6

-29.61 = x - 122.6

-29.61 + 122.6 = x

x = 92.99