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The SAT mathematics scores in the state of Florida for this year 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 score lies between 500 and 700? Express your answer as a decimal.

Respuesta :

The answer to the problem presented above is .475. Using the empirical rule, the probability that a randomly selected score lies between 500 and 700 (which is 2 standard deviations above the mean) is .475 or 47.5%. 

Answer:

0.4772

Step-by-step explanation:

Mean = [tex]\mu = 500[/tex]

Standard deviation = [tex]\sigma = 100[/tex]

Now we are supposed to find  the probability that a randomly selected score lies between 500 and 700.

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

At x = 500

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

[tex]z=\frac{0}{100}[/tex]

At x = 700

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

[tex]z=\frac{200}{100}[/tex]

[tex]z=2[/tex]

Now to find P(500<z<700)

P(0<z<2) =P(z<2)-P(z<0)

Now using z table :

P(z<2)-P(z<0) =0.9772-0.5000=0.4772

Thus the probability that a randomly selected score lies between 500 and 700 is 0.4772.

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