The national average for IQ scores is 100, and the standard deviation is 15. The distribution of IQ scores is bell-shaped. What percentage of students have an IQ score less than 92?

Question

High School

We appreciate your visit to The national average for IQ scores is 100 and the standard deviation is 15 The distribution of IQ scores is bell shaped What percentage of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

AlbertFrancis AlbertFrancis · Answer 1 · 2024-03-20T18:22:56-04:00

Approximately 29.50% of students have an IQ score less than 92.

To find the percentage of students with an IQ score less than 92, we can use the normal distribution and the z-score formula.

The z-score measures how many standard deviations a particular value is from the mean.

First, we need to convert the IQ score of 92 to a z-score.

The formula is: z = (x - µ) / σ { where x is the given value, µ is the mean, and σ is the standard deviation }.

In this case, x = 92, µ = 100, and σ = 15.

Plugging in the values, we get:

z = (92 - 100) / 15 = -0.5333

Using a z-table or calculator, we can find the area under the curve to the left of z = -0.5333.

This gives us the percentage of students with an IQ score less than 92.

According to the z-table, the area to the left of z = -0.5333 is approximately 0.2950.

Therefore, approximately 29.50% of students have an IQ score less than 92.