Question

The SAT mathematics scores in the state of Florida 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 student’s math score is between 300 and 700? Express your answer as a decimal.

Answer 1

Since the range of the scores given was between 300 and 700 (which is 2 standard deviations below and above the mean), the probability that a randomly selected student's math score - as based on the empirical rule of statistics - is 95%. In decimal form, it is .95. 

Answer 2

Answer:

0.9544

Step-by-step explanation:

Mean = $\mu = 500$

Standard deviation = $\sigma = 100$

Formula of z score : $z = \frac{x-\mu}{\sigma}$  -- 1

Now we are supposed to find  the probability that a randomly selected student’s math score is between 300 and 700

So, Substitute x = 300 in 1

$z = \frac{300-500}{100}$

$z =-2$

Substitute x = 700

$z = \frac{700-500}{100}$

$z =2$

So, P(-2<z<2)

P(z<2)-P(z<-2)

Using the z table substitute the values .0228

=0.9772-0.0228

=0.9544

So,  the probability that a randomly selected student’s math score is between 300 and 700 is 0.9544