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.

The interval \((300,700)\) corresponds to the part of the distribution lying within 2 standard deviations of the mean (since 500-2100=300 and 500+2100=700). The empirical rule states that approximately 95% of the distribution is expected to fall in this range.

Answer Link

pinquancaro pinquancaro · Answer 2 · 2019-06-06T03:03:01-04:00

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

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

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.