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 2 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