Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals μ=105 and a standard deviation sigma equals σ=15. Find the probability that a randomly selected adult has an IQ less than 135.

Answer 1

The probability that a randomly selected adult has an IQ less than

135 is 0.97725

Step-by-step explanation:

Assume that adults have IQ scores that are normally distributed with a mean of mu equals μ = 105 and a standard deviation sigma equals σ = 15

We need to find the probability that a randomly selected adult has an IQ less than 135

For the probability that X < b;

• Convert b into a z-score using z = (X - μ)/σ, where μ is the mean and σ is the standard deviation
• Use the normal distribution table of z to find the area to the left of the z-value ⇒ P(X < b)

∵ z = (X - μ)/σ

∵ μ = 105 , σ = 15 and X = 135

∴ $z=\frac{135-105}{15}=2$

- Use z-table to find the area corresponding to z-score of 2

∵ The area to the left of z-score of 2 = 0.97725

∴ P(X < 136) = 0.97725

The probability that a randomly selected adult has an IQ less than

135 is 0.97725

Learn more:

You can learn more about probability in brainly.com/question/4625002

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