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Mathematics

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Gnoma [55]3 years ago

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Draw arrow to -2.5 hope this helps

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The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with

likoan [24]

Answer:

Percentage of students who scored greater than 700 = 97.72%

Step-by-step explanation:

We are given that the College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100.

Let X = percentage of students who scored greater than 700.

Since, X ~ N( $\mu, \sigma^{2}$ )

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1) where, $\mu$ = 500 and $\sigma$ = 100

So, P(percentage of students who scored greater than 700) = P(X > 700)

P(X > 700) = P( $\frac{X-\mu}{\sigma}$ < $\frac{700-500}{100}$ ) = P(Z < 2) = 0.97725 or 97.72% Therefore, percentage of students who scored greater than 700 is 97.72%.