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.
2. Use the tabulated values of the standard normal variable (z table) in order to figure outvalues of z1 and z2 as shown in the following figure:
a. z1 =
b. z2 =
3. Calculate following probabilities (area under the curve) for the standard normal variable, z:
a. P(-∞ ≤ z ≤ 1.01) =
b. P(0 ≤ z ≤ 2.5) =
c. P(-∞ ≤ z ≤ ∞) =
d. P(-1.25 ≤ z ≤ 3.19) =
e. P(-∞ ≤ z ≤ -0.44) =
4. Mean of 10 observations is 100. One of the observations is dropped from the data. Meanof the remaining observations is 9. What is the value of the dropped observation?
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:
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Statement
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True
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False
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39% of the total variation in Y can be explained by predictors included in
the regression model.
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X1 is a significant predictor of Y.
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Holding X2 constant, a one unit increase in X1 raises Y by 0.56 units.
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Predicted value of Y is 0 when X1 and X2 are simultaneously 0.
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The intercept is not significantly different from 0 in the population.
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6. Fill in all unshaded boxes with missing numbers in the following table. This problem willtest your understanding of several principles related to elementary statistics and algebraic operationsinvolving the summation notation.
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X
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Y
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X2
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Y2
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X+Y
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(X-X¯)
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(X-X¯)2
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X/Y
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36
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4
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8
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3
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-1
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9
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0
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-5
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2
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Sum
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15
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8
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15
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Mean
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7. Evaluate expressions a through e using information about variables X and Y from thefollowing table.
a. Σ( X -Y ) =
b. Σ X -Y =
c. [Σ (X -Y)]2 =
d. (ΣX)2(ΣY)2=
e. ΣX ( X -Y ) =
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 thenexactly three are of each color?