Question

Estimate the number of DVDs that will be checked out for every 100 patrons.

Answer 1

The number of DVDs that will be checked out for every 100 patrons will be 20.

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

 

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

The expected value of X will be:

$E(X) = np$

The information is given in the table.

The probability of getting DVDs will be

$\rm p = \dfrac{2}{10}\\\\p=2$

The value of n is 100.

Then the number of DVDs that will be checked out for every 100 patrons will be

$\rm E(X) = 100 \times 0.2\\\\E(X) = 20$

Learn more about binomial distribution here:

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