A random sample of size 1,000 is taken from a population where p = .20.What is ?
A).006
B).20
C).02
D).16

Question

A random sample of size 1,000 is taken from a population where p = .20.What is  ?
A).006 
B).20 
C).02 
D).16

Quizplus · Accepted Answer

In a binomial distribution, the mean is equal to the probability of success (p). Therefore, the expected value for the proportion of successes in a sample of size 1,000 from a population with p = 0.20 is 0.20. So, there is a 20% chance of success for any given trial, and 11 trials would have an expected value of 2.20. The probability of getting exactly 11 successes in a sample of 1,000 can be calculated using the binomial probability formula, but since this formula involves factorials and is time-consuming, it is easier to use a binomial calculator. Using such a calculator, we find that the probability of getting 11 or fewer successes is approximately 0.2003, which is closest to choice B (0.20).

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