Question

For which sample size (n) and sample proportion (p) can a normal curve be

used to approximate the sampling distribution?

Answer 1

Option c.

Explanation:

Using the normal curve to approximate a sampling distribution:

For a sample size n and a proportion n, the normal curve can be used if:

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

Option a:

`np = 35*0.8 = 28 > 10`

`n(1-p) = 35*0.2 = 7 < 10`

So option a cannot be used.

Option b:

`np = 65*0.9 = 58.5 > 10`

`n(1-p) = 65*0.1 = 6.5 < 10`

So option b cannot be used.

Option c:

`np = 65*0.8 = 52 > 10`

`n(1-p) = 65*0.2 = 13 > 10`

So option c can be used, and is the answer

Option d:

`np = 35*0.9 = 31.5 > 10`

`n(1-p) = 35*0.1 = 3.5 < 10`

So option d cannot be used.

The answer is given by option c.