Populations and Samples

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Variability of Samples from Distributions

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

$P\left(X=x\right)$P(X=x) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

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.

Round your answer to two decimal places.

Easy

Approx 9 minutes

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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

Use statistical methods to make a formal inference