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Assume that adults have IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15. Find the probability that a randomly selected adult has an IQ score greater than 120.

User Wolfr
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Final answer:

To find the probability that a randomly selected adult has an IQ score greater than 120, we can use the standard normal distribution and standardize the IQ scores. The probability is approximately 0.0918, or 9.18%.

Step-by-step explanation:

To find the probability that a randomly selected adult has an IQ score greater than 120, we can standardize the IQ scores to a standard normal distribution and then use the standard normal table. The formula to standardize a value X from a normal distribution with mean μ and standard deviation σ is z = (X - μ) / σ.

Using the given information, the standardized value for an IQ score of 120 is z = (120 - 100) / 15 = 1.33. We want to find the probability that a randomly selected adult has an IQ score greater than 120, which is equivalent to finding the area to the right of z = 1.33 in the standard normal distribution.

Referring to the standard normal table, the area to the right of z = 1.33 is approximately 0.0918.

Therefore, the probability that a randomly selected adult has an IQ score greater than 120 is approximately 0.0918, or 9.18%.

User Reden
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