1. Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with = 6 ounces and = 2.5 ounces. If a sample size of 15 is selected, what is mean of the sampling distribution (the distribution of X-bar)?

2. The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, 11.77. Referring to the above, a 99% confidence interval for the mean voltage of the power packs is from __________ to __________.

3. Suppose that customers arrive at a bank's ATM at the exponentially distributed mean rate of 30 per hour. If a customer has just arrived, what is the probability that the next customer will arrive within the next 3 minutes?

4. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What percentage of the plan recipients die before they reach the standard retirement age of 65?