sampling distribution

**anonymousgirl** · September 15th 2008, 12:34 AM

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?

**mr fantastic** · September 15th 2008, 01:22 AM

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.

**anonymousgirl** · September 15th 2008, 03:49 AM

wow tq

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