The distribution of reading scale scores in the 4th grade at Roosevelt Elementary School - The distribution of reading scale scores in the 4th grade at Roosevelt Elementary School was approximately normal with mean \mu = 221 and standard deviation \sigma = 36. Students must score in the top 20% to be eligible for participation in the gifted program. What is the minimum reading scale score for students to be eligible for the gifted program?

Sangeetha Pulapaka (last edited 10 months ago) (Expert, Educator @Qalaxia)

The normal distribution has mean μ=221 and standard deviation σ=36

Since we are looking at the top 20%, we want to find the reading scale score such that the area under the curve to its right is 0.2.

First, we must determine the z-score with an area of 0.2 above it.

Since the z-score with an area of 0.2 above it is the same as the z-score with an area of 0.8 below it, we use the z- table to determine the approximate z-score we are looking for.

We select a z-score closest to 0.8. So the z-value for this will be 0.8+ 0.05 = 0.85.

Now we use

We know that

z = \frac{x - \mu}{\sigma}

Plugging in the known values and solving for x we get

0.85 = \frac{x - 221}{36}

x -221 = 0.85 \times 36

x = 251.6

x\approx 252