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The SAT mathematics scores in the state of Florida for this year are approximately normally distributed with a mean of 500 and a standard deviation of 100.

Using the empirical rule, what is the probability that a randomly selected score lies between 500 and 700? Express your answer as a decimal.

Verified Answer :

The answer to the problem presented above is .475. Using the empirical rule, the probability that a randomly selected score lies between 500 and 700 (which is 2 standard deviations above the mean) is .475 or 47.5%.

Answer:

0.4772

Step-by-step explanation:

Mean = \(\mu = 500\)

Standard deviation = \(\sigma = 100\)

Now we are supposed to find  the probability that a randomly selected score lies between 500 and 700.

Formula : \(z=\frac{x-\mu}{\sigma}\)

At x = 500

\(z=\frac{500-500}{100}\)

\(z=\frac{0}{100}\)

At x = 700

\(z=\frac{700-500}{100}\)

\(z=\frac{200}{100}\)

\(z=2\)

Now to find P(500<z<700)

P(0<z<2) =P(z<2)-P(z<0)

Now using z table :

P(z<2)-P(z<0) =0.9772-0.5000=0.4772

Thus the probability that a randomly selected score lies between 500 and 700 is 0.4772.

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