Question

If 8% of all people in a certain region are unemployed, find the probability that in a sample of 200 people, there are fewer than 10 people who are unemployed. ( approximate Binomial by Normal Distribution )

Answer 1

Here we have

n=200 and p=0.08

Since np = 16 and n(1-p) = 184 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

The z-score for X = 10-0.5 = 9.5 is

The required probability is:

Answer: 0.0455