1. A question on a proficiency test is multiple choice with four possible answers, one of which is correct. Assuming that all responses are random guesses, find the porbability that among 12 test subjects, exactly five answer the question correctly.
2. Find the mean and standard deviation for a binomial distribution with 412 trials and a probability of success of 0.86 and enter the answers below. Round each answer to one decimal place. A. find mean B. find standard dev
3. In a standard normal distribution, what is the probability of a z-score being greater than -0.85?
4. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?
5. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches.What is the probability of selecting a bolt at random that has a diameter larger than 0.328 inches?
6. Forty-Five percent of the people that get mail-order catalogs order something. Find the probability that less than four of 10 people getting these catalogs will order something.
7. The probability that a house in an urban area will be burglarized is 1%. If 20 houses are randomly selected, what is the probability that less than 2 of the houses will be burglarized?
8. The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150.What is the probability that a trainee selected at random earns less than $900 a month?