New Zealand
Level 8 - NCEA Level 3

# The approximate normal distribution of the sample proportions

## Interactive practice questions

A survey was carried out to investigate the number of teachers in Australian schools who like using the chalkboard to teach. This survey found that in a sample of $1222$1222 teachers, $321$321 liked using the chalkboard, while the rest did not.

a

Calculate the sample proportion of $\hat{p}$^p, of those teachers surveyed who like using the chalkboard.

Write your answer correct to $3$3 decimal places.

b

Using your answer from part (a), estimate the standard deviation, $\hat{\sigma}$^σ, of the random variable $\hat{P}$^P, for such samples of size $1222$1222.

Round your answer to $3$3 decimal places.

Easy
Approx 4 minutes

Lachlan wanted to know the proportion of commuters that regularly listen to music on his train. In his carriage, he found that in a sample of $35$35 commuters, $7$7 were listening to music.

A survey involving $218$218 midwives found that $150$150 of them were aged between $46$46 and $60$60 years.

To practice her archery, Sandy marked a small interval on the board with length $5$5 centimetres. Sandy takes $240$240 shots at the board from a certain distance, with $151$151 landing between the small interval.

### 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