1. Define a random variable - 2. Draw four cards from a deck of regular playing cards, replacing the cards and shuffling the cards between draws. Compute the probability of drawing a heart, diamond, club, and spade in that order. 3. Your firm has 3 different manufacturing lines that each produce the same type of widget. There is a 85 percent chance that each line is functional on any given day. Assuming a Bernoulli process what is the probability of all three manufacturing lines working on any given day? 4. An airline has classified its customers as high-volume travelers (assumed to be business travelers) or low-volume travelers (assumed to be leisure travelers). Seventy-five (75) percent are high volume travelers. If five people are randomly selected from a list of customers, what is the probability all are high-volume (leisure) travelers? 5. The weekly incomes of shift foreman for a given industry follow a normal probability distribution. With a mean of $1,000 and a standard deviation of $100, what is the z-value for the income (called X) of a foreman who earns $1100 per week? For a foreman who earns $900 per week? In words, what do your results indicate? 6. The weekly incomes of shift foreman for a given industry follow a normal probability distribution. With a mean of $1,000 and a standard deviation of $100, what is the area under the curve between $840 and $1200? In words, what do your results indicate? 7. Define a continuous random variable and provide an example