Question

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

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<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 .