The President’s Economic Advisory Council publishes an economic forecast every y

Question

The President’s Economic Advisory Council publishes an economic forecast every year. In the latest report, a normal distribution is used to describe the possible percentage change in US GDP (Gross Domestic Product) for the upcoming year. The distribution is centered on a growth rate of 4.2% and has known a standard deviation of 0.7%. According to this distribution, how likely is it that the change in GDP will be

a. less than 3.5%?

b. between 3.8% and 5.0%?

c. greater than 6.0%?

d. between 4.5% and 5.5%?

Explanation / Answer

Mean = 4.2%

Standard deviation = 0.7%

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(X < 3.5%) = P(Z < (3.5 - 4.2)/0.7)

= P(Z < -1)

= 0.1587

b) P(3.8 < X < 5.0) = P(X < 5.0) - P(X < 3.8)

= P(Z < (5.0 - 4.2)/0.7) - P(Z < (3.8 - 4.2)/0.7)

= P(Z < 1.14) - P(Z < -0.57)

= 0.8729 - 0.2843

= 0.5886

c) P(X > 6.0) = 1 - P(X < 6.0)

= 1 - P(Z < (6.0 - 4.2)/0.7)

= 1 - P(Z < 2.57)

= 1 - 0.9949

= 0.0051

d) P(4.5 < X < 5.5) = P(X < 5.5) - P(X < 4.5)

= P(Z < (5.5-4.2)/0.7) - P(Z < (4.5 - 4.2)/0.7)

= P(Z < 1.86) - P(Z < 0.43)

= 0.9686 - 0.6664

= 0.3022

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