Help 3 1. Define a random variable. 2. Draw three 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, and club in that order. 3. Your firm has 4 different manufacturing lines that each produce the same type of widget. There is a 95 percent chance that each line is functional on any given day. Assuming a Bernoulli process what is the probability of all four 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). Sixty-five (65) percent are high volume travelers. If five people are randomly selected from a list of customers, what is the probability all are low-volume (leisure) travelers? 5. The weekly incomes of shift foreman for a given industry follow a normal probability distribution. With a mean of $1,100 and a standard deviation of $100, what is the z-value for the income (called X) of a foreman who earns $1150 per week? For a foreman who earns $975 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 discrete variable and provide an example