Question

The annual per capita consumption of ice cream (in pounds) in the United States is approximately Normal with mean of μ=20.7 pounds and standard deviation σ=4.2 pounds.

1. What percentage of United States citizens eat more than 22 pounds of ice cream each year?

2. What percentage of United States citizens eat between 15 and 20 pounds of ice cream each year?

Please show work

Answer 1

Given,

= 20.7 , = 4.2

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

a)

P(X > 22) = P(Z > ( 22 - 20.7 ) / 4.2)

= P(Z > 0.31)

= 1 - P(Z < 0.31)

= 1 - 0.6217 (From Z table)

= 0.3783

= 37.83%

b)

P(15 < X < 20) = P(X < 20) - P(X < 15)

= P(Z < (20 - 20.7 ) / 4.2) - P(Z < ( 15 - 20.7 ) / 4.2)

= P(Z < -0.17) - P(Z < -1.36)

= 0.4325 - 0.0869 (From Z table)

= 0.3456

= 34.56%