Populations and Samples

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

Central limit theorem

The weights of eggs at a particular egg farm are determined to be normally distributed with a mean of $65.7$65.7 grams and a standard deviation of $1.2$1.2 grams.

a

Many egg samples of size $100$100 are taken and measured, and the means of each of the samples, $\overline{X}$`X` are calculated.

What type of distribution does $\overline{X}$`X` represent?

Exponential Distribution

A

Discrete Uniform Distribution

B

Normal Distribution

C

Continuous Uniform Distribution

D

Exponential Distribution

A

Discrete Uniform Distribution

B

Normal Distribution

C

Continuous Uniform Distribution

D

b

Calculate the mean of $\overline{X}$`X`.

c

Calculate the standard deviation of $\overline{X}$`X` corresponding to a sample size of $100$100. Round your answer to $2$2 decimal places.

Easy

Approx 4 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