Question

Data from 2011 show that 45.6% of all flights from IAH departed late. If an analyst takes a simple random sample of 400 flights, what can be said about the sampling distribution of the sample proportion of flights that departed late?

1. The sampling distribution will be approximately uniform with a mean of 45.6

2. The sampling distribution will be approximately normal with a mean of 0.456 and a standard deviation of

   0.025.

3. The sampling distribution will be approximately normal with a mean of 45.6 and a standard deviation of

   99.2.

4. The sampling distribution of the sample proportion will be binomial with p = .4 and n = 400.

Answer 1

The correct option is C

Explanation:

μ = p = 0.456

σ ​​​= √p(1−p)​​ /n = 0.0249 = 0.025

The sampling distribution will be approx normal with a mean of 0.456 and a standard deviation of 0.025.