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.

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

- 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%**

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