New Zealand
Level 8 - NCEA Level 3

# Problems with Binomial Distributions

## 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

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
Less than a minute

Which of the following statements is true?

Consider the binomial probability formula

$P\left(x\right)=\nCr{n}{x}p^x\left(1-p\right)^{n-x}$P(x)=nCxpx(1p)nx,

where $P\left(x\right)$P(x) is the probability of obtaining $x$x successes in $n$n independent trials.

A particular nationwide numeracy test has a failure rate of $30%$30%.

If you randomly selected $100$100 students from across the country to do the test, how many would you expect to pass?

### Outcomes

#### S8-4

Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

#### 91586

Apply probability distributions in solving problems