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

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

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=(x-\mu)/(\sigma)`

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

For x = 300 substitute in the formula,

`z = (300-500)/(100)\\\\z =-2`

For x = 700 substitute in the formula,

`z = (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.