Question

Find the mean and standard deviation for the following, where possible,if not.explain why it is not.

a. x P(x) b. x P(x) c. x P(x)

0 0.1 -9 0.15 0 0.34

1 0.2 10 0.45 1 0.23

2 0.3 11 0.38 2 0.17

3 0.4   12 -0.21 3 0.26

-4 0.3

d. In a poll of 12 to 18yr. old females, conducted by theNokTerNoh!Magazine editor,Carolyn(Zleep D’Pri’D), found that 27%of them said that they expected to see a female soccer player on a team in the Men’s World Cup within 10 years. A random sample of 12 females from this age group was selected, by use of the formula;findi.P(Exactly 8 females share this view) (4pts)ii.P(Between 5-7 share this view) (6pts)

Answer 1

a) In this question, first we need to make sure if the given P(x) is valid. It is valid if

x	P(x)
0	0.1
1	0.2
2	0.3
3	0.4
-4	0.3

Here = 0.1+0.2+0.3+0.4+0.3 = 1.3 .

Hence this is invalid.

x	P(x)
-9	0.15
10	0.45
11	0.38
12	-0.21

Since P(x) are probabilities and probabilities lie between [0,1]. Here, P(12) = -0.21 < 0. Hence this is not valid.

x	P(x)
0	0.34
1	0.23
2	0.17
3	0.26

= 0.34+0.23+0.17+0.26 = 1 and all P(x) lies between [0,1]. Hence this is a valid probabillity mass function.

Mean =E[X] =   = 0*0.34 + 1*0.23 + 2*0.17 * 3*0.26 = 1.35

Now, = = 0*0.34 + 1*0.23 + 4*0.17 * 9*0.26 = 3.25

Var(X) = = 3.25 - 1.35^2 = 1.4275

standard deviation = = = 1.194

b) Given 27% expect to see a female. So p = 0.27

From n = 12 females, we have to find,

i. P(Exactly 8 females share this view)

ii. P(Between 5-7 share this view)

Let X be the number of females share this view, then X ~ B(12,0.27)

i. P(Exactly 8 females share this view) = P(X=8)

= 12C8 (0.27)^8 (1-0.27)^4 = 0.00397 ~ 0.004

ii. P(Between 5-7 share this view) = P(X=5) + P(X=6) + P(X=7)

= 12C5 (0.27)^5 (1-0.27)^7 + 12C6 (0.27)^6 (1-0.27)^6 + 12C7 (0.27)^7 (1-0.27)^5

= 0.126 + 0.054 + 0.017 = 0.197