Question

If p = .8 and n = 50, then we can conclude that the sampling distribution of pˆ is approximately a normal distribution

Answer 1

Yes we can conclude.

Explanation:

The sampling distribution of
`\hat{p}` can be approximated as a Normal Distribution only if:

np and nq are both equal to or greater than 10. i.e.

• np ≥ 10
• nq ≥ 10

Both of these conditions must be met in order to approximate the sampling distribution of
`\hat{p}` as Normal Distribution.

From the given data:

n = 50

p = 0.80

q = 1 - p = 1 - 0.80 = 0.20

np = 50(0.80) = 40

nq = 50(0.20) = 10

This means the conditions that np and nq must be equal to or greater than 10 is being satisfied. So, we can conclude that the sampling distribution of pˆ is approximately a normal distribution