Matthew plays basketball for his high school. On average, he scores 33 points per game, with a standard deviation of 2 points. W
hat 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.
Note: Assume that a Normal model is appropriate for the distribution of points.
2 answers:
<h3>Answer: Choice B</h3>
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
which isn't too far off from the 0.15%
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b) Using the probability mass function we got:
Step-by-step explanation:
Previous concepts
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Solution to the problem
Part a
For this case we define the random variable X="number of car owners in a random sample of 12 who get the maintenance service done on their cars according to the schedule recommended by the auto company". And for this case the distribution for X is:
And the possible values for the random variable are X=0,1,2,3,4,5,6,7,8,9,10,11,12
Part b
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Using the probability mass function we got: