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Levart [38]
3 years ago
5

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation equals σ=20. Find

the probability that a randomly selected adult has an IQ less than 137.

Mathematics
1 answer:
GuDViN [60]3 years ago
7 0

Probability that a randomly selected adult has an IQ less than 137 is 0.9452

<u>Step-by-step explanation:</u>

<u>Step 1: </u>

Sketch the curve.

The probability that X<137 is equal to the blue area under the curve.

<u>Step 2: </u>

Since μ=105 and σ=20 we have:

P ( X<137 )=P ( X−μ<137−105 )= P(X−μ/ σ< 137−105/20 )

Since x−μ/σ=Z and 137−105/20=1.6 we have:

P (X<137)=P (Z<1.6)

<u>Step 3: </u>

Use the standard normal table to conclude that:

P (Z<1.6)=0.9452

∴ probability that a randomly selected adult has an IQ less than 137 is 0.9452.

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