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------------------------------------------------ Assume that adults have IQ scores that are normally distributed with a mean of 99.9 and a standard deviation of 15.3.

Find the probability that a randomly selected adult has an IQ greater than 120.5.

(Hint: Draw a graph.)

The probability that a randomly selected adult from this group has an IQ greater than 120.5 is __________. (Round to four decimal places as needed.)

To find the probability, we need to calculate the area under the normal distribution curve corresponding to IQ scores greater than 120.5. We can do this by standardizing the IQ score and using the standard normal distribution table or a statistical calculator.

Given:

Mean (μ) = 99.9

Standard deviation (σ) = 15.3

IQ score (X) = 120.5

First, we standardize the IQ score using the formula:

Z = (X - μ) / σ

Z = (120.5 - 99.9) / 15.3

≈ 1.343

Next, we find the area under the standard normal distribution curve to the right of Z = 1.343. Using a standard normal distribution table or a statistical calculator, we find the corresponding area to be approximately 0.0916.

However, we are interested in the probability of an IQ score greater than 120.5, which includes the area to the right of 120.5. Since the standard normal distribution is symmetric, we can subtract the area to the right of Z = 1.343 from 0.5 (which represents the area under the entire curve) to get the desired probability.

Probability = 0.5 - 0.0916

≈ 0.4084

Therefore, the probability that a randomly selected adult from this group has an IQ greater than 120.5 is approximately 0.4084.

The probability that a randomly selected adult from the given group has an IQ greater than 120.5 is approximately 0.4084.

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