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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
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The area of the shaded region is (Round to four decimal places as needed.)
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Find the area of the shaded region The graph to the right depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standar class=

Respuesta :

JeanaShupp

Answer: 0.4255

Step-by-step explanation:

Given:  IQ scores of adults, and those scores are normally distributed

Mean: [tex]\mu=100[/tex]

Standard deviation: [tex]\sigma= 15[/tex]

Let X denotes the IQ of a random adults.

The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]

[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]

Hence, area between 102 and 130 = 0.4255

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