ANSWER
C. 145.75 yd²
EXPLANATION
First we need to calculate the area of the four triangular faces.
The lateral surface area
The area of the base is
To find the total surface area, we add the area of the square base to the area of the 4 triangular faces.
Therefore the total surface area is
Matthew will score less than 27 points in about 0.15% of his basketball games.
=======================================================
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%
