Question

The number of ships to arrive at a harbor on any given day is a random variable represented by x. The probability distribution of x is as follows. (Give your answers correct to two decimal places.) x 10 11 12 13 14 P(x) 0.31 0.07 0.14 0.06 0.42 (a) Find the mean of the number of ships that arrive at a harbor on a given day. 12.21 Correct: Your answer is correct. (b) Find the standard deviation, σ, of the number of ships that arrive at a harbor on a given day. x= 10,11,12,13,14 P(x)= 0.31, 0.07, 0.14, 0.06, 0.42

Answer 1

X	P(X)	X * P(X)
10	0.31	3.1	31
11	0.07	0.77	8.47
12	0.14	1.68	20.16
13	0.06	0.78	10.14
14	0.42	5.88	82.32

a) Expected value of X is,

Therefore, the mean of the number of ships that arrive at a harbor on a given day is 12.21

b) Standard deviation of X is,

Therefore, the standard deviation of the number of ships that arrive at a harbor on a given day is 1.7338