Question

If a population proportion is believed to be 0.60, how many items must be sampled to ensure that the sampling distribution of the sample proportion will be approximately normal

Answer 1

`n \geq 42`

Explanation:

Data provided

P = 0.6

The calculation of sample size is shown below:-

Here the sampling distribution of proportion will be approximately normal, then follow the rule which is here below:-

`np\geq 10\ and\ np (1 - p)\geq 10`

Now we will consider condition 2

`np(1 - p)\geq \ 10`

`n(0.6) (1 - 0.6) \geq \ 10`

`n(0.6) (0.4) \geq\ 10`

`n\geq (10)/(0.24)`

`n \geq 41.66667`

or

`n \geq 42`

Therefore for computing the required sample size we simply solve the above equation.