Question

It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met

Answer 1

Random sample,
`np \geq 10` and
`n(1-p) \geq 10`, so yes, both conditions were satisfied.

Explanation:

60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.

This means that
`p = 0.6`

A recent survey was conducted from 1000 of these individuals.

This means that
`n = 1000`

Also, a random sample, so the first condition was satisfied.

The sample size must be large (so that at least 10 or more successes and failures).

`np = 1000*0.6 = 600 \geq 10`

`n(1-p) = 1000*0.4 = 400 \geq 10`

So yes, both conditions were met.