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NemiM [27]
3 years ago
15

Assume that adults have IQ scores that are normally distributed with a mean of 96 and a standard deviation of 15.7. Find the pro

bability that randomly selected adults has and IQ greater than 123.4
Mathematics
1 answer:
astraxan [27]3 years ago
7 0

Answer:

4.05% probability that a randomly selected adult has an IQ greater than 123.4.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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

Z = \frac{X - \mu}{\sigma}

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.

In this question, we have that:

\mu = 96, \sigma = 15.7

Probability that a randomly selected adult has an IQ greater than 123.4.

This is 1 subtracted by the pvalue of Z when X = 123.4. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{123.4 - 96}{15.7}

Z = 1.745

Z = 1.745 has a pvalue of 0.9595

1 - 0.9595 = 0.0405

4.05% probability that a randomly selected adult has an IQ greater than 123.4.

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