Question

reading improvement program to help students improve their reading, a school district decides to implement a reading program. it is to be administered to the bottom 6% 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 116.5, find the cutoff score that will make a student eligible for the program. the standard deviation is 23. assume the variable is normally distributed. use the standard normal distribution table. round z - value calculations to 2 decimal places and the final answer to the nearest whole number. cutoff score =

Explanation:

Step1: Find the z - score

We want to find the z - score corresponding to the bottom 6% (or 0.06) of the normal distribution. Looking up 0.06 in the standard normal distribution table (the area to the left of the z - score is 0.06). The closest z - score is \(z=-1.55\) (from the standard normal table).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 116.5\), \(\sigma=23\), and \(z=-1.55\).
We solve for \(x\):

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Answer:

\(81\)