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2. In 2012, the mean SAT math score was 514, and the standard deviation was 117. For the purposes of this question, assume that the scores were normally distributed.
Using a graphing calculator, and without using zz-scores, find the probability (rounded to the nearest thousandth), and explain how the answer was determined that a randomly
selected SAT math student in 2012 scored
a. Between 400 and 480.
b. Less than 350.

Respuesta :

Answer:

a) [tex] P(400 < X < 480) = 0.221[/tex]

We can use the following excel code to find the answer:

"=NORM.DIST(480,514,117,TRUE)-NORM.DIST(400,514,117,TRUE)"

The other possibility is with the command normalcdf on the ti84 plus calculator, by this procedure:

Press 2nd > press VARS > DISTR  > select  normalcdf > Enter the following:

normalcdf(400 ,480,514,117)

And press equal.

b) [tex] P(X < 350) = 0.0805[/tex]

We can use the following excel code to find the answer:

"=NORM.DIST(350,514,117,TRUE)"

The other possibility is with the command normalcdf on the ti84 plus calculator, by this procedure:

Press 2nd > press VARS > DISTR  > select  normalcdf > Enter the following:

normalcdf(-1000000,350,514,117)

And press equal.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

For this case we have that our random variable is given by:

[tex]X \sim N (\mu = 514, \sigma =117)[/tex]

And we want to find these probabilities:

Part a

[tex] P(400 < X < 480) = 0.221[/tex]

We can use the following excel code to find the answer:

"=NORM.DIST(480,514,117,TRUE)-NORM.DIST(400,514,117,TRUE)"

The other possibility is with the command normalcdf on the ti84 plus calculator, by this procedure:

Press 2nd > press VARS > DISTR  > select  normalcdf > Enter the following:

normalcdf(400 ,480,514,117)

And press equal.

Part b

[tex] P(X < 350) = 0.0805[/tex]

We can use the following excel code to find the answer:

"=NORM.DIST(350,514,117,TRUE)"

The other possibility is with the command normalcdf on the ti84 plus calculator, by this procedure:

Press 2nd > press VARS > DISTR  > select  normalcdf > Enter the following:

normalcdf(-1000000,350,514,117)

And press equal.

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