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

I this the answer you are looking for would probably be 47.7%. hope this helps!!

Answer 2

Answer:

The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.

Step-by-step explanation:

We have given that, The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100.

To find : What is the probability that a randomly selected student’s math score is between 300 and 700?

Solution :

The mean is $\mu=500$

The standard deviation is  $\sigma=1000$

Formula to find z-score is

$z=\frac{x-\mu}{\sigma}$

Now, we have to find the probability score is between 300 and 700              

For x = 300 substitute in the formula,

$z = \frac{300-500}{100}\\\\z =-2$

For x = 700 substitute in the formula,

$z = \frac{700-500}{100}\\\\z =2$

Now, The probability between P(-2<z<2)  is written as

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

Using the z table substitute the values of z

At z<-2 is 0.228 and at z<2 is 0.9772.

$P(-2<z<2)=0.9772-0.0228$

$P(-2<z<2)=0.9544$

Therefore, The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.