A random sample of size 1,000 is taken from a population where p = .20.Find P(

Question

A random sample of size 1,000 is taken from a population where p = .20.Find P(  < .18).
A).9429 
B).0571 
C).2643 
D).0793

Quizplus · Accepted Answer

We can use the normal approximation to the binomial distribution since n*p = 1,000*0.20 = 200 and n*(1-p) = 1,000*0.80 = 800 are both greater than 10. The mean of the sampling distribution is given by mu = p = 0.20 and the standard deviation is given by sigma = sqrt(p*(1-p)/n) = sqrt(0.20*0.80/1,000) = 0.014. So, we need to standardize the value (0.18 - 0.20)/0.014 = -1.43 and find the area to the left of that value under the standard normal distribution. Using a standard normal table or calculator, we find the probability to be P(Z < -1.43) = 0.0766. Therefore, the answer is B) 0.0571 (rounded to four decimal places).

A Random Sample of Size 1,000 Is Taken from a Population