NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Bernoulli mean and variance

## Interactive practice questions

$X$X is a binomial random variable with parameters $n=35$n=35 and $p=0.8$p=0.8.

a

Find $E\left(X\right)$E(X).

b

Find $Var\left(X\right)$Var(X).

Easy
Approx a minute

A science exam consisted of $75$75 multiple choice questions, each with $5$5 possible options. Bart guessed the answers to all the questions at random.

Let $X$X be the number of questions Bart gets correct.

Ten Bernoulli trials are conducted and the expected value is $9$9.

A research study found that professional football players successfully kicked penalty goals $72%$72% of the time. Frank kicked $49$49 penalty goals in his career.

Let the number of penalty goals Frank missed be $X$X.

### 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