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Assume that adults have IQ scores that are normally distributed with a mean of 100.2 and a standard deviation of 20.1.

Find the probability that a randomly selected adult has an IQ greater than 138.8. (Hint: Draw a graph.)

The probability that a randomly selected adult from this group has an IQ greater than 138.8 is (round to four decimal places as needed).

Answer :

Final answer:

To find the probability that a randomly selected adult has an IQ greater than 138.8, we need to standardize the value using the formula z = (x - μ) / σ. The probability is approximately 0.0276.

Explanation:

To find the probability that a randomly selected adult has an IQ greater than 138.8, we need to standardize the value using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, we have x = 138.8, μ = 100.2, and σ = 20.1. Plugging in the values, we get z = (138.8 - 100.2) / 20.1 = 1.920. We can then use a standard normal distribution table or a calculator to find the area to the right of this z-value. The probability that a randomly selected adult has an IQ greater than 138.8 is approximately 0.0276 rounded to four decimal places.

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