Information about "Probabilities"

Can you answer these problems and show work.

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

2. Suppose a family plans 6 children, and the probability that a particular child is a girl is ½. Find the probabilities that the 6-child family has at least 4 girls.

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

4. Give the probability that corresponds to the shaded region of the histogram.

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

6. A certain machine that is used to manufacture screws produces a defect rate of 0.01. A random sample of 20 screws is selected. Find the probabilities that the sample contains exactly 3 defective screws.

7. The number of units carried in one semester by students in a business mathematics class was as follows. Use intervals 9-10, 11-12, 13-14, 15-16 to do the following:(a) write a frequency distribution; (b) draw a histogram; (c) draw a frequency polygon
10 9 16 12 13 15 13 16 15 11 13
12 12 15 12 14 10 12 14 15 15 13

(a) write a frequency distribution

(b) draw a histogram

(c) draw a frequency polygon

8. Find the mean for the following.
105, 108, 110, 115, 106, 110, 104, 113, 117

9. Find the mean for the following.
Interval Frequency
40-44 2
45-49 5
50-54 7
55-59 10
60-64 4
65-69 1

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

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

12. Find the area under the standard normal curve between z = 0 and z = 1.27.

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

14. The probability that a small business will go bankrupt in its first year is 0.21. For 50 such small business, find the following probabilities by using either the binomial probability formula or by using the normal approximation.

a. Exactly 8 go bankrupt.

b. No more than 2 go bankrupt.

15. How are the variance and the standard deviation of a distribution related? What is measured by the standard deviation?

16. What is meant by a skewed distribution?