Question

1.Suppose that the number of cans of soda pop filled in a day at a bottling plant is a random variable with an expected value of 10,000 and a variance of 1000. UseChebyshev's Inequality to obtain a lower bound on the probability that the plant will fill between 9000 and 11,000 cans on a particular day.

Answer 1

(a)

Consider at a bottling plant, a random variable with an expected value is 10,000.

Consider a variance of 1000.

Suppose the plant will fill more than 11,000 cans on a particular day.

The objective is to use Markov’s Inequality to obtain an upper bound on the probability.

Let X is the random variable that count the number of cans of soda pop filled in a day.

The expected value

And the variance is

From Markov’s inequality,

Here is a sample space and is a random variable.

And the value of is 11,000.

The probability that the plant will fill more than 11,000 cans is.

(b)

Consider the plant will fill between 9000 and 11000 cans on a particular day.

The objective is to use Chebyshev’s Inequality to obtain a lower bound on the probability.

Recollect the Chebyshev’s Inequality,

Here is a positive real number and is equal to 1000.

Here is the sample space and

And the variance is

Apply Chebyshev’s Inequality with

The probability that the plant will fill between 9000 and 11000 cans is

Answer 2

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