Question

Suppose we have N = 6 values from a population. These values are 4, 8, 0, 10, 14 and 6. Let μ and σ denote the population mean and population standard deviation of these six values, respectively.

(a) What are the values of μ and σ, respectively?

μ = 4.8580; σ = 7

μ = 7; σ = 4.8580

μ = 7; σ = 4.4347

μ = 7; σ = 19.6667

μ = 7; σ = 23.6

(b) What percentage of the six population values stated above, fall within the interval (μ - σ, μ + σ) ?

66.66%

100%

50%

83.33%

16.66%

Consider a 42-ball lottery game. In total there are 42 balls numbered 1 through to 42 inclusive. Three balls are drawn (chosen randomly), one at a time, without replacement (so that a ball cannot be chosen more than once). To win the grand prize, a lottery player must have the same numbers selected as those that are drawn. The order of the numbers is not important so that if a lottery player has chosen the combination 20, 21, 22 and, in order, the numbers 21, 20, 22 are drawn, then the lottery player will win the grand prize (to be shared with other grand prize winners). You can assume that each ball has exactly the same chance of being drawn as each of the others.

(a) Consider the 42-ball lottery game described above. In how many different ways can you select a sample of three balls from a population of 42 balls?

1654895

14

105900

11480

42

(b) Consider the 42-ball lottery game described above. Recall that the order of the numbers chosen is not important and that each number can only be chosen once. In total, how many combinations are there available that include the numbers 20 and 21 but NOT the number 23?

40

14

42

3

39

Answer 1

b. The number of different combinations that are available which include the number 20 and 21 but not 23 given by:

40 ways.

Since, ball numbered 20 and 21 are selected then 1 ball is selected from remaining 40 balls.