Solve the below:
Q1) The distribution of actual weights of 8 oz. wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.
a) If a sample of five of these cheese wedges is selected, the probability that their average weight is less than 8 oz is?
b) There is only a 5% chance that the average weight of the sample of five of the cheese wedges will be below?
Q2) In an instant lottery, your chances of winning are 0.2. If you play the lottery five times and outcomes are independent, the probability that you win at most once is?
Q3) At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college are selected. Let X denote the number of Hispanics among them.
a) Find the mean of X a)
b) Find the standard deviation of X b)