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Linear Operators - Mean, Median, Mode and Z-Scores

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Week 4 Quiz (covering Chapters 8 - Counting Principles; Further probability Topics and 9 - Statistics)

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Show your work (Show the formula, the values of the variables in the formula, and the result of the formula.).

1. How many variations in first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners?

2. In a Chinese restaurant, the menu lists 8 items in Column A and 6 items in column B. To order a dinner, the diner is told to select 3 items from column A and 2 from column B. How many dinners are possible?

3. Suppose a family plans 6 children, and the probability that a particular child is a girl is 1/2. Find the probability that the 6 child family has exactly 2 girls.

4. Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probability that both cards are aces.

5. You pay $6 to play a game where you will roll a die, with a payoff as follows: $8 for a 6, $7 for a 5, and $4 for any other result. What are your expected winnings? Is the game fair?

6. Find the mean for: 105, 108, 110, 115, 106, 110, 104, 113, 117.

7. Find the median and mode (or modes) for: 32, 35, 36, 44, 46, 46, 59.

8. Find the range and standard deviation for: 14, 17, 18, 19, 32.

9. Find the following area under the standard normal curve: between z=-1.88 and z=2.10.

10. Find a z-score such that 8% of the area under the curve is to the right of z.

EC. A machine that fills quart orange juice bottles is set to fill them with 32.1 oz. If the actual contents of the cartons vary normally, with a standard deviation of .1 oz, what percent of the cartons contain less than a quart (32 oz).

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Solution Summary

Complete, Neat and Step-by-step Solutions for (Q8 to Q10 and EC) are provided.

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Solutions (Q8 to Q10 and EC):

(8) (a) Range = Max score - Min score = 32 - 14 = 18

(b) SD
x d = x - Mean d^2
14 -6 ...

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