# Math Help - sampling distribution

1. ## sampling distribution

In a large city 1 person in 5 is left-handed.
a. Find the most likely number of left-handed people in a random sample of 6 people.
b. Find the mean and the standard deviation of the number of left-handed people in a
random sample of 25 people.
c. How large must a random sample be if the probability that it contains at least one lefthanded
person is to be greater than 0.95?

2. Originally Posted by anonymousgirl
In a large city 1 person in 5 is left-handed.
a. Find the most likely number of left-handed people in a random sample of 6 people.
b. Find the mean and the standard deviation of the number of left-handed people in a
random sample of 25 people.
c. How large must a random sample be if the probability that it contains at least one lefthanded
person is to be greater than 0.95?
a. Let X be the random variable number of left handed people in a random sample of 6.

X ~ Binomial (n = 6, p = 1/5)

E(X) = ..... ?

b. Let Y be the random variable number of left handed people in a random sample of 25.

Y ~ Binomial (n = 25, p = 1/5)

E(Y) = ..... ?

Var(Y) = .... ?

c. Let W be the random variable number of left handed people in a random sample of n.

W ~ Binomial (n = ?, p = 1/5)

Require the smallest value of n such that

$\Pr(W \geq 1) > 0.95$

$\Rightarrow 1 - \Pr(W = 0) > 0.95$

$\Rightarrow \Pr(W = 0) < 0.05$

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

Find the smallest value of n that satisfies this inequality.

3. wow tq