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Find the area of the shaded region. The graph below depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Find the area of the shaded region The graph below depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard devia class=

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Answer:

  0.7475

Step-by-step explanation:

A suitable calculator can show the area under the curve is 0.7475.

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The percentage of the shaded area under the curve is about 74.8%

Step-by-step explanation:

Given the Parameters :

  • Mean, μ = 100
  • Standard deviation, σ = 15
  • Score, X = 110

Recall :

Zscore = (X - μ) ÷ σ

Zscore = (110 - 100) / 15

Zscore = 10 / 15 = 0.667

The shaded region is the percentage of the area under the curve less than the Zscore of 0.667

Using a normal distribution table :

P(Z < 0.667) = 0.74761

The percentage of the area under the curve is 74.8% .

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