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Assume that adults have IQ scores that are normally distributed with a mean of 97.9 and a standard deviation of 19.6. Find the probability that a randomly selected adult has an IQ greater than 126.5. ​(Hint: Draw a​ graph.)

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Final answer:

The question is about finding the probability of an adult having an IQ above a certain value, given the mean and standard deviation of the IQ distribution. The method involves calculating the z-score and then using a standard normal distribution table or calculator to find the probability.

Step-by-step explanation:

The subject of the question is Mathematics, and it is at the College level. The task is to calculate the probability that a randomly selected adult has an IQ greater than 126.5, given that adult IQ scores are normally distributed with a mean of 97.9 and a standard deviation of 19.6.

To find this probability, we would first need to calculate the z-score for an IQ of 126.5, which is done by subtracting the mean from the IQ score and then dividing the result by the standard deviation. The z-score expresses how many standard deviations a data point is from the mean. Once the z-score is obtained, we can use a standard normal distribution table or a calculator with normal distribution functions to find the corresponding probability.

Here is the formula for the z-score:

z = (X - μ) / σ

where X is the IQ score in question, μ is the mean, and σ is the standard deviation.

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