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 =

X = 71

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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.

This means that

Calculate the IQ below which a child would be eligible to apply for this education assistance program (X).

Bottom 5%, so the 5th percentile and below, we want to find the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

As a whole number, X = 71

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step-by-step explanation: