The annual profits of small business owners in the town of Brownville has a normal distribution with mean $50,000 and standard deviation $4000.
Calculate z-scores for the following four profits: $35,000, $40,000, $38,000, and $50,000.
What proportion of the distribution falls below the profit of $45,000?
What proportion of the distribution falls between the profits of $45,000 and $50,000?
What proportion of the distribution falls above the profit of $45,000?
What proportion of the distribution falls between the profit of $35,000 and $52,000?
What proportion of the distribution falls between the profit of $37,000 and $55,000?
[Hint: Remember when I am asking proportion, I mean the area under the curve in proportion as provided in the Normal Curve Table at the back of the Book. In the cases, when I ask percentage, you need to covert the proportion into percentage].
A business person is selected at random from this population to serve on the board to review profits. What is the probability that his or her average profits exceeds $45,000? [Hint: Remember that the normal curve can be thought of as a probability distribution]