Question

1. One of the calculations we do this week is the “expected value” or mean of a distribution.

a. In your non-math life, what does “expected” mean to you? Answer in 1 – 5 complete sentences.

b. What does “expected value” mean in a probability/statistics situation? How is it calculated? Answer in complete sentences, please (not math; use words).

2. Suppose we have a Normal distribution with mean 35 and standard deviation 4.

a. Take a few minutes to draw this curve very neatly and accurately. Reference the document “How to Draw a Normal Curve” in this assessment.

Use a separate sheet of paper, or add extra space here, and use a straightedge to draw an axis.

b. Label your curve from part a with the 68-95-99.7 Rule.

c. If we randomly select a value from this Normal model and call that value x, find:

i.              P(x < 30)

ii.             P(x > 30.4)

iii.            P(33 < x < 40)

Make a note about how you’re doing your calculations (Ti-8x, GeoGebra, Excel, etc.) and what you enter.

d. The middle 90% of the Normal curve is between what two values? (We’re looking for a symmetric interval here, so 45% is above the mean and 45% below the mean.)

Answer 1

1.

(a) Expected means likely or which has the possibility to happen. It is  believed to be going to happen or arrive.

(b) The expected value is a predicted value of a variable. It is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur, and summing all of those values.

2.

4-a 0 47 CHean 9s (About 997% osa-ahons lie, Wittt3(SD) \ 4

(d)

The middle 90% under a bell curve is the middle section of the bell curve that excludes the 5% of the area on the left and 5% of the area on the right.