The number of DVDs that will be checked out for every 100 patrons will be 20.
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
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value of X will be:
[tex]E(X) = np\\[/tex]
The information is given in the table.
The probability of getting DVDs will be
[tex]\rm p = \dfrac{2}{10}\\\\p=2[/tex]
The value of n is 100.
Then the number of DVDs that will be checked out for every 100 patrons will be
[tex]\rm E(X) = 100 \times 0.2\\\\E(X) = 20[/tex]
Learn more about binomial distribution here:
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