reading improvement program to help students improve their reading, a school district decides to implement a…

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 =

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 =

Answer

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): [ \begin{align*}

  • 1.55&=\frac{x - 116.5}{23}\ x-116.5&=-1.55\times23\ x-116.5&=-35.65\ x&=116.5- 35.65\ x&=80.85 \end{align*} ]

Answer:

(81)