Question

Part 1

A. I roll a pair of dice.  What is the expected value of the outcome?

B. I roll a pair of dice.  What is the standard deviation associated with the outcome?

Part 2

A. I buy 16 tropical fish of the species “cichlisoma negrofasciata.”  I cannot determine the gender of the fish, but I’m told there is a 53% probability of a single fish being a female.  Construct the appropriate probability distribution, with outcomes of 0 females to 16 females.

B. What is the probability of there being six or fewer females?

C. What is the probability of there being more than nine females?

D. What is the expected number of females?

E. What is the standard deviation of the number of females?

Answer 1

part 1:-

(a)

Fair Die
Roll	Probability
1	1/6
2	1/6
3	1/6
4	1/6
5	1/6
6	1/6

Mean or Expected Value = (1) (1/6) + (2) (1/6) + (3) (1/6) + (4) (1/6) + (5) (1/6) + (6) (1/6) = 3.5

(b)

Roll	R−μ	(R−μ)2	Probability	(R−μ)2x Probability
1	1 – 3.5 = -2.5	(−2.5)2=6.25	1/6	6.25 x (1/6)
2	2 – 3.5 = -1.5	(−1.5)2=2.25	1/6	2.25 x (1/6)
3	3 – 3.5 = -0.5	(–0.5)2=0.25	1/6	0.25 x (1/6)
4	4 – 3.5 = 0.5	(0.5)2=0.25	1/6	0.25 x (1/6)
5	5 – 3.5 = 1.5	(1.5)2=2.25	1/6	2.25 x (1/6)
6	6 – 3.5 = 2.5	(2.5)2=6.25	1/6	6.25 x (1/6)
SUM				2.917
				sqrt(2.917) = 1.71

Standard Deviation=  = 1.71