Question

A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?

Answer 1

`\mu = 5.2`

`\sigma = 2.257`

Explanation:

Given

`n = 260` -- samples

`p = (1)/(50)` --- one in 50

Solving (a): The mean

This is calculated as:

`\mu = np`

`\mu = 260 * (1)/(50)`

`\mu = 5.2`

Solving (b): The standard deviation

This is calculated as:

`\sigma = √(\mu * (1-p))`

`\sigma = √(5.2 * (1-1/50))`

`\sigma = √(5.2 * 0.98)`

`\sigma = √(5.096)`

`\sigma = 2.257`