New Zealand
Level 8 - NCEA Level 3

# Variability of Samples from Distributions

## Interactive practice questions

Consider a fair $8$8 sided die with faces labeled from $1$1 to $8$8.

Let $X$X be the outcome when the die is rolled.

a

Complete the table of values for the probability distribution for $X$X.

 $x$x $P\left(X=x\right)$P(X=x) $1$1 $2$2 $3$3 $4$4 $5$5 $6$6 $7$7 $8$8 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Calculate the mean of the distribution.

c

Calculate the standard deviation of the distribution correct to two decimal places.

d

The die was rolled 20 times with the following results

 $8$8 $3$3 $3$3 $5$5 $4$4 $8$8 $1$1 $7$7 $6$6 $5$5 $2$2 $2$2 $3$3 $5$5 $4$4 $3$3 $8$8 $6$6 $5$5 $1$1

Calculate the sample mean of the results.

e

Calculate the sample standard deviation.

Easy
Approx 9 minutes

The random variable $X$X is uniformly distributed with a variance of $\frac{25}{12}$2512 over the interval $1\le x\le6$1x6.

$R$R is a binomial variable with $n=14$n=14 and $p=0.25$p=0.25.

Two samples, $A$A and $B$B, each of size $10$10, are taken from $R$R and tabulated below.

The normal variable $X$X has a mean of $120$120 and a standard deviation of $15$15.

Two samples, $A$A and $B$B, each of size $10$10, are taken from $X$X and tabulated below.

### 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