The binomial random variable X counts the number of married students in a random sample of high school seniors, where p 0.02 of all high school seniors are married. The random variable is for the proportion of married students in the sample.
a. If X = 3 in a random sample of 100 students, find . p
b. If in a random sample of 200 students, find X.
c. Find the mean and standard deviation of X if the sample consists of n = 50 students. (Round to the nearest tenth.)
d. Interpret the mean and standard deviation found in part (c).
e. Find the mean and standard deviation of if the sample consists of n = 50 students. (Round to the nearest hundredth.)
f. Find the mean and standard deviation of X if the sample consists of n = 500 students. (Round to the nearest tenth.)
g. Find the mean and standard deviation of if the sample consists of n = 500 students. (Round to the nearest hundredth.)
h. Interpret the mean and standard deviation found in part (g).
i. In which case does our sample proportion tend to come closer to the population proportion 0.02: for samples of 50 or 500 or both the same?