Question

The United States exports hundreds of thousands of metric tons of wood chips to Japan each year. The amount exported varies from year to year with an approximately Normal distribution with a mean of 278 thousand metric tons and standard deviation of 56 thousand metric tons.

In what percent of years does the U.S. export between 250 and 350 thousand metric tons to Japan?

Answer 1

solution:

mean number of wood chips =

standard deviation =

so we have to find the proportion percentage of between 250 and 350 thousand metric tons.

using normal probability formula

P(250 < X < 350) = P(X < 350) - P(X < 250)

for x = 250 , z score is calculated as below

for x = 350,

P(250 < X < 350) = (value of z to the left of 1.29) - (value of z to the left of -0.5)

P(250 < X < 350) = 0.9015 - 0.3085 = 0.593

so proportion of year in which between 250 and 350 thousand metric ton exported = 59.3%