Question

(1 point) The amount of paper used in a year per person in America has a normal (bell-shaped)distribution with a mean of 650 pounds and a standard deviation of 150pounds.

a)What percent of Americans use between200 and 1100 pounds of paper per year?

b)What percent of Americans use more than 800 pounds of paper per year?

c)What percent of Americans use more than 350 pounds of paper per year?

Answer 1

Solution :

Given that ,

mean = = 650

standard deviation = = 150

a)

P(200 < x < 1100) = P((200 - 650)/ 150) < (x - ) /  < (1100 - 650) / 150) )

= P(-3 < z < 3)

= P(z < 3) - P(z < -3)

= 0.9987 - 0.0013 Using standard normal table,  

99.87 percent of Americans use between200 and 1100 pounds of paper per year.

b)

P(x > 800) = 1 - P(x < 800)

= 1 - P((x - ) / < (800 - 650) / 150)

= 1 - P(z < 1)

= 1 - 0.8413 Using standard normal table.

= 0.1587

15.87 percent of Americans use more than 800 pounds of paper per year.

c)

P(x > 350) = 1 - P(x < 350)

= 1 - P((x - ) / < (350 - 650) / 150)

= 1 - P(z < -2)

= 1 - 0.0228 Using standard normal table.

= 0.9772

97.72 percent of Americans use more than 350 pounds of paper per year.