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 =

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