is the distribution of means for samples of size n from a population with mean υ and standard deviation ¤.In the formulas below, X is the distribution of counts in the binomial setting with trial of size n and is the distribution of means for samples of size n from a population with mean υ and standard deviation ¤.
1. According to government data, 25% of employed women have never been married. What is the probability that in a random sample of 10 employed women exactly 2 have never been married?
Solution: the distribution of unmarried women in a sample of 10 chosen independently is binomial. From the table the probability that exactly 2 out of 10 have never been married is
2. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean υ = 298 ml and standard deviation ¤ = 3 ml. What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml?
Solution: the observed value 
ml corresponds to a z-score of
According to the normal distribution table, the probability that z is this low or lower is 0.0071.