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

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<X<130 is equal to the blue area under the curve.

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<X<130 ) = P ( 0.67<Z<2 )

Step 3: Use the standard normal table to conclude that:

P ( 0.67<Z<2 )=0.2286

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

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step-by-step explanation:

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