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

The interval $(300,700)$ corresponds to the part of the distribution lying within 2 standard deviations of the mean (since 500-2*100=300 and 500+2*100=700). The empirical rule states that approximately 95% of the distribution is expected to fall in this range.

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:

Given : 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 $\sigma=100$

Formula to find z-score is

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

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

Substitute x = 300 in the formula,

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

$z =-2$

Substitute x = 700 in the formula,

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

$z =2$

So, the probability between $P(-2$

$P(z$

Using the z table substitute the values of z at -2 and 2.

P=0.9772-0.0228

P=0.9544

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