SOLUTION: Each Filipino uses an average of 650 pounds of plastic in a year. Suppose that the distribution is approximately normal with a population standard deviation of 153.5 pounds. Assume

Question 1205782: Each Filipino uses an average of 650 pounds of plastic in a year. Suppose that the distribution is approximately normal with a population standard deviation of 153.5 pounds. Assume the variable is normally distributed. Find the probability that a randomly selected Filipino uses
a.) More than 800 pounds of paper in a year (10 points)
b.) Less than 400 pounds a year (10 points)
c.) Between 500 and 700 pounds a year (10 points)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
population mean is 650 and population standard deviation is 153.5.

z-score formula is z = (x-m)/s

in this problem:

x is the value of the randomly selected variable.
m is the population mean
s is the standard deviation.
z is the z-score.

answers to your questions are shown below.

Find the probability that a randomly selected Filipino uses

a.) More than 800 pounds of paper in a year (10 points)

for x = 800, z = (800 - 650) / 153.5 = .9771986971.

area to the right of this z-score is equal to .1642.
that's the probability that a random selected filipino uses more than 800 pounds of plastic in a year.

b.) Less than 400 pounds a year (10 points)

for x = 400, z = (400 - 650) / 153.5 = -1.628664495.

area to the left of this z-score is equal to .0517.
that's the probability that a randomly selected filipino uses less than 400 pounds of plastic in a year.

c.) Between 500 and 700 pounds a year (10 points)
.
for x = 500, z = (500 - 650) / 153.5 = -.9771986971.
for x = 700, z = (700 - 650) / 153.5 = .325732899.

area in between these two z-score is equal to .4635.
that's the probability that a randomly selected filipino uses between 500 and 700 pounds of plastic in a year.

calculator used can be found at https://davidmlane.com/hyperstat/z_table.html

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