Question

Matthew plays basketball for his high school. On average, he scores 33 points per game, with a standard deviation of 2 points. What percentage of basketball games will result in Matthew scoring less than 27 points?
Note: Assume that a Normal model is appropriate for the distribution of points.

Answer 1

Answer:

I believe is the correct answer

Step-by-step explanation:

a

Answer 2

Answer: Choice B

Matthew will score less than 27 points in about 0.15% of his basketball games.

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Explanation:

mu = 33 = population mean

sigma = 2 = population standard deviation

Let's find the z score when x = 27

z = (x - mu)/sigma

z = (27-33)/2

z = -6/2

z = -3

A score of 27 points is exactly three standard deviation units below the mean of 33 points.

Now refer to the Empirical Rule chart shown below. Notice that roughly 99.7% of the entire population is within 3 standard deviations of the mean. This is the span from z = -3 to z = 3.

That leaves about 100% - 99.7% = 0.3% left over for the two tails combined.

One tail has about (0.3%)/2 = 0.15% of the total area, and therefor about 0.15% of the total games will have Matthew scoring less than 27 points. This is an estimate of course.

To get a more accurate answer, you can use a Z table to find that

$P(Z < -3) \approx 0.00135 \approx 0.135\%$

which isn't too far off from the 0.15%