College

We appreciate your visit to The education department of state is interested in funding an education assistance program for 12 year old children whose intelligence quotients lie in the bottom. 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!

The education department of state is interested in funding an education assistance program for 12 year-old children whose intelligence quotients lie in the bottom 5% of the population. According to national data, the IQ's of the 12 year-old population are normally distributed with a mean of 96 and a standard deviation of 15.

Calculate the IQ below which a child would be eligible to apply for this education assistance program (X). You may find this standard normal table useful. Give your answer as a whole number.

X =

Answer :

The IQ below which a child would be eligible to apply for the education assistance program is 71.

To find the IQ below which a child would be eligible to apply for the education assistance program, we need to find the value of X such that it corresponds to the bottom 5% of the normal distribution of IQ scores.

Given data:

Mean (μ) = 96

Standard Deviation (σ) = 15

Use the standard normal distribution (Z-score) formula to find the value of X:

Z = (X - μ) / σ

In this case, we want to find the Z-score that corresponds to the 5th percentile, which is -1.645 according to the standard normal distribution table.

Now we can solve for X:

-1.645 = (X - 96) / 15

Solving for X:

X - 96 = -1.645 × 15

X - 96 = -24.675

Add 96 on both sides:

X = 96 - 24.675

X = 71.325

Hence, the IQ below which a child would be eligible to apply for the education assistance program is approximately 71.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ12

Thanks for taking the time to read The education department of state is interested in funding an education assistance program for 12 year old children whose intelligence quotients lie in the bottom. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada