Question

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 500 and a standard deviation of 80. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores.

How high should a student score be to win this award? Give your answer to the nearest integer.

Answer 1

An eighth-grade student would need to score at least 602 on the standardized reading exam to be in the top 10% and win the award, when rounding the calculated score to the nearest integer.

Step-by-step explanation:

To determine how high an eighth grade student's score must be to win an award for scoring in the top 10% of a standardized reading exam, we need to find the z-score that corresponds to the top 10% of the normal distribution. Since the scores are normally distributed with a mean (μ) of 500 and a standard deviation (σ) of 80, we can use the z-table to find the z-score that corresponds to the 90th percentile (the cutoff for the top 10%).

Looking up the z-table, we find that a z-score of approximately 1.28 corresponds to the 90th percentile. Using the z-score formula:

Z = (X - μ) / σ

where X is the score we want to find, we can rearrange the formula to solve for X:

X = Z * σ + μ

Substituting the values, we get:

X = 1.28 * 80 + 500

X = 102.4 + 500

X = 602.4

Rounding to the nearest integer, an eighth-grade student would need a score of 602 to be in the top 10% and win the award.