Dr. Horton is an avid coffee drinker. By observing Dr. Horton on randomly selected days, Dr. Ziggy came to the conclusion that Dr. Horton drinks one "XXXL" coffee on 30% of all days, and two "XXXL" coffees on 70% of all days. Given Dr. Ziggy's finding, let X be a random variable for the number of coffees that Dr. Horton drinks on any given day with the following probability distribution:
X: 12 P(X = x): 0.3 0.7
- What is the mean, variance, and standard deviation of the number of coffees consumed per day?
- Let ????¯ be a random variable for the sample mean number of coffees consumed over n = 5 randomly selected days. What are the mean and standard deviation of this sample mean?