Answer:
The slope is -2, the y-intercept is 12
Step-by-step explanation:
Chose any two coordinates pair. Let's make use of:
Thus,
Using the slope-intercept equation, find the y-intercept, b, as follows:
Use any coordinate pair as x and y, then solve for b.
Let's use (3, 6)
Add 6 to both sides
The slope (m) of the linear function that is represented by the table is -2, while the y-intercept (b), is 12.
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%
