In a normal distribution, 75% of the items are under 100 and 20% are over 200. Find the mean and...

1. In a normal distribution, 75% of the items are under 100 and 20% are over 200. Find the mean and standard deviation of the distribution.

1. Use the tabulated values of the standard normal variable (z table) in order to figure out values of z1 and z2 as shown in the following figure:

a. z1 =

b. z2 =

1. 3. Calculate following probabilities (area under the curve) for the standard normal variable, z:
   1. P(–∞ ≤ z ≤ 1.01) =
   2. P(0 ≤ z ≤ 2.5) =
   3. P(–∞ ≤ z ≤ ∞) =
   4. P(–1.25 ≤ z ≤ 3.19) =
   5. P(–∞ ≤ z ≤ –0.44) =

1. 4.  Mean of 10 observations is 100. One of the observations is dropped from the data. Mean of the remaining observations is 9. What is the value of the dropped observation?

1. 5. The following results were obtained from a multiple regression model predicting Y from X1 and X2.

Indicate whether each of the following statements is true or false:

1. 6. Fill in all unshaded boxes with missing numbers in the following table. This problem will test your understanding of several principles related to elementary statistics and algebraic operations involving the summation notation.

1. 7. Evaluate expressions a through e using information about variables X and Y from the following table.

1. Σ( X −Y ) =
2. Σ X −Y =
3. [Σ (X –Y)]² =
4. (Σ^X)²(Σ^Y)²=
5. ΣX ( X −Y ) =

1. 8. Consider an urn that contains 40 balls. Of these 20 are red, 10 are green, and the remaining are blue. What is the probability that if nine balls are randomly selected from the urn then exactly three are of each color?