# Thread: Help me again, urgent

1. ## Help me again, urgent

In a large city 1 person in 5 is left handed.
i) find probability that in a random sample of 10 people exactly 3 will be left handed
ii) find the most likely number of left handed people in a random sample of 12 people
iii) find the mean and standard deviation of the number of left handed people in a random sample of 25 people
iv) How large must a random sample be if the probability that it contains at least one left handed person is to be greater than 0.95?

2. Originally Posted by whleow
In a large city 1 person in 5 is left handed.
i) find probability that in a random sample of 10 people exactly 3 will be left handed
ii) find the most likely number of left handed people in a random sample of 12 people
iii) find the mean and standard deviation of the number of left handed people in a random sample of 25 people
iv) How large must a random sample be if the probability that it contains at least one left handed person is to be greater than 0.95?
i) n=10, p=0.2,
P(X=3)= 10C3x $(0.2)^3$x $(0.8)^7$

= 0.201326592

ii) mean= E(X) = np = 12x0.2= 2.4 or 2 people.

iii)mean = E(X) = np = 25x0.2 = 5 people.
S.D. = (Var(X))^0.5 = (np(1-p))^0.5 = (25x0.2x0.8)^0.5 = 2

iv) Problem
I'm stuck here, I got this far:

1-(P(X=0))=0.95 which goes to

0.05=(P(X=0))

0.05=n(1-p)

0.05=n(0.8)

n=0.0625...?

Where did I go wrong?

3. Originally Posted by Nyoxis
i) n=10, p=0.2,
P(X=3)= 10C3x $(0.2)^3$x $(0.8)^7$

= 0.201326592

ii) mean= E(X) = np = 12x0.2= 2.4 or 2 people.

iii)mean = E(X) = np = 25x0.2 = 5 people.
S.D. = (Var(X))^0.5 = (np(1-p))^0.5 = (25x0.2x0.8)^0.5 = 2

iv) Problem
I'm stuck here, I got this far:

1-(P(X=0))=0.95 which goes to

0.05=(P(X=0))

0.05=n(1-p)

0.05=n(0.8)

n=0.0625...?

Where did I go wrong?
The smallest integer value of n satisfying the following is required:

$\Pr(X = 0) \leq 0.05$

$\Rightarrow {n \choose 0} p^0 (1 - p)^n \leq 0.05$

$\Rightarrow (1) (1) \left( 1 - \frac{1}{5} \right)^n \leq 0.05$

$\Rightarrow \left( \frac{4}{5} \right)^n \leq 0.05$

$\Rightarrow n = 14$.