NZ Level 8 (NZC) Level 3 (NCEA) [In development] Sample means and population means

## Interactive practice questions

A random number generator, generates random integers, $X$X, between $43$43 and $65$65 with equal probability.

a

What type of probability distribution does this scenario represent?

Uniform continuous probability distribution

A

Uniform discrete probability distribution

B

Uniform continuous probability distribution

A

Uniform discrete probability distribution

B
b

What is the mean or expected value of this distribution of generated random numbers?

c

A sample of $10$10 numbers are generated and shown below.

$43,49,62,57,47,64,58,50,59,47$43,49,62,57,47,64,58,50,59,47

Calculate the mean of this sample data.

Easy
Approx 3 minutes

A spinner is split into $5$5 equal sections, and these sections are numbered from $1$1 to $5$5. The spinner is used to generated random integers, $X$X, between $1$1 and $5$5 with equal probability.

The position $X$X that a raindrop falls on the interval $\left[0,8\right]$[0,8] in metres is found to be equally likely for all possible $x$x.

In 2016, the mean result of all Western Australian students sitting the Mathematics Methods exam was $58%$58%, with a standard deviation of $15%$15%. A sample of $15$15 students were chosen at random and their results are shown below.

$56.07,49.91,34.32,83.07,57.22,82.88,27.42,65.28,61.43,38.35,70.6,66.46,36.51,67,46.93$56.07,49.91,34.32,83.07,57.22,82.88,27.42,65.28,61.43,38.35,70.6,66.46,36.51,67,46.93

### Outcomes

#### S8-2

Make inferences from surveys and experiments: A determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem B using methods such as resampling or randomisation to assess

#### 91582

Use statistical methods to make a formal inference