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Assume that adults have IQ scores that are normally distributed with a mean of 101.9 and a standard deviation of 22.7. Find the probability that a randomly selected adult has an IQ greater than 131.0. ​(Hint: Draw a​ graph.)

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Final answer:

To determine the probability that an adult has an IQ greater than 131, calculate the z-score using the mean (101.9) and standard deviation (22.7), and then find the corresponding probability from a z-table or a statistical calculator.

Step-by-step explanation:

To find the probability that a randomly selected adult has an IQ greater than 131, we use the given mean IQ score of 101.9 and a standard deviation of 22.7. This is a problem involving the normal distribution. We need to calculate the z-score for an IQ of 131, which is done using the formula z = (X - μ) / σ, where X is the IQ score in question, μ is the mean, and σ is the standard deviation.

The z-score represents how many standard deviations away from the mean our IQ value of 131 is. After calculating the z-score, we consult a z-table or use a statistical calculator to find the probability associated with that z-score. The area to the right of the z-score will give us the desired probability that an adult has an IQ higher than 131.

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