Respuesta :

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 .

The probability that the person's IQ falls between 110 and 130 is 0.2286.

Calculation of the probability:

Since the mean and the standard deviation is 100 and 15

So,

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

[tex]P ( (110-100)\div 15 < (X-\mu)\div\sigma < (130-100)\div 15)[/tex]

Now

Since

[tex]Z = (x-\mu)\div \sigma , (110-100)\div 15 = 0.67\ and\ (130-100)\div 15 = 2[/tex]

So,

P ( 110<X<130 ) = P ( 0.67<Z<2 )

Now we use the standard normal table i.e.

= P ( 0.67<Z<2 )

=0.2286

Therefore, The probability that the person's IQ falls between 110 and 130 is 0.2286.

Learn more about mean here: https://brainly.com/question/10132345

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