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7.06 Binomial distribution

Interactive practice questions

Which of the following statements is true?

In a binomial experiment, there are $n$n repeated, dependent trials.

A

In a binomial experiment, there are $n$n repeated, independent trials.

B

In a binomial experiment, there are exactly two trials.

C

In a binomial experiment, there is exactly one trial.

D
Easy
< 1min

Which of the following statements is true?

Easy
< 1min

Does rolling a six-sided die $20$20 times and counting the number of times the die lands on $1$1 describe a binomial random variable?

Easy
< 1min

Can the sum of the outcomes of rolling a six-sided die $10$10 times describe a binomial random variable?

Easy
< 1min
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Outcomes

ACMMM147

understand the concepts of Bernoulli trials and the concept of a binomial random variable as the number of ‘successes’ in n independent Bernoulli trials, with the same probability of success p in each trial

ACMMM148

identify contexts suitable for modelling by binomial random variables

ACMMM149

determine and use the probabilities P(X=r)=(nr)p^r(1−p)^(n−r) associated with the binomial distribution with parameters n and p; note the mean np and variance np(1−p) of a binomial distribution

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