Question

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.

Answer 1

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.

Answer 2

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%.