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 [tex](300,700)[/tex] 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.

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pinquancaro pinquancaro · Answer 2 · 2019-06-06T09:03:01+02:00

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 [tex]\mu=500[/tex]

The standard deviation is [tex]\sigma=100[/tex]

Formula to find z-score is

[tex]z=\frac{x-\mu}{\sigma}[/tex]

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,

[tex]z = \frac{300-500}{100}[/tex]

[tex]z =-2[/tex]

Substitute x = 700 in the formula,

[tex]z = \frac{700-500}{100}[/tex]

[tex]z =2[/tex]

So, the probability between [tex]P(-2<z<2)[/tex]

[tex]P(z<2)-P(z<-2)[/tex]

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.