Iq scores are normally distributed with a mean of 100 and a standard deviation of 15 if one person is randomly selected what is the probability that the persons IQ falls between 110 and 130

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Mathematics

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13 March, 08:19

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15 if one person is randomly selected what is the probability that the persons IQ falls between 110 and 130

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Brennen Yang · Answer 1

probability that the persons IQ falls between 110 and 130 is 0.2286.

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that 110
Step 2:

Since μ=100 and σ=15 we have:

P (110 < X < 130) = P (110-100 < X-μ < 130-100)

⇒ P ((110-100) / 15< (X-μ) / σ< (130-100) / 15)

Since Z = (x-μ) / σ, (110-100) / 15 = 0.67 and (130-100) / 15 = 2 we have:

P (110
Step 3: Use the standard normal table to conclude that:

P (0.67
Therefore, probability that the persons IQ falls between 110 and 130 is 0.2286.