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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 19.5 Find the probability that a randomly selected adult has an IQ greater than 131.9 (Hint Draw a graph.) The probability that a randomly selected adult from this group has an IQ greater than 131.9 is (Round to four decimal places as needed.)

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Final answer:

To calculate the probability that a randomly selected adult has an IQ greater than 131.9, first find the z-score using the formula z = (X - μ) / σ, then use the standard normal distribution table to find the corresponding probability.

Step-by-step explanation:

The student's question pertains to finding the probability that a randomly selected adult has an IQ score greater than 131.9, given that IQ scores are normally distributed with a mean (μ) of 100.2 and a standard deviation (σ) of 19.5. The calculation of this probability involves finding the z-score and then using the standard normal distribution table to find the corresponding probability.

To find the z-score, we use the formula: z = (X - μ) / σ, where X is the value in question (131.9 in this case). Plugging in the values, we get z = (131.9 - 100.2) / 19.5.

Once the z-score is calculated, consult the standard normal distribution table (or a calculator with the normal distribution function) to find the area to the right of this z-score, which represents the probability that a randomly selected adult has an IQ greater than 131.9. Since tables typically give the area to the left, you will need to subtract this value from 1 to obtain the probability we're looking for. Remember to round the result to four decimal places as needed.

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