Assignment:
Counting Principles: Further Probability Topics
Q1. A basket contains 4 black, 2 blue and 5 green balls. A sample of 3 balls is drawn. Find the probabilities taht the sample contains the following: 2 black balls and 1 green ball
Q2. Suppose a family plans 6 children and the probability that a particular child is a girl is 1/2 Find the probabilities that the 6-child family has the following children; Exactly 3 girls
Q3. Suppose 2 cards are drawn without replacement from an ordinary deck of 52 find the probalities of the following results; At least one is a face card.
Q4. Six students will decide which of them are on a committee by flipping a coin. Each student flips the coin and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all 6 students?
Q5. A cerain machine that is used to manfacture screws produces a defect rate of .01. a random sample of 20 screw is selected. Find the probabilites that the sample contains the following; exactly 3 defective screws.
Statistics
Q1. Find the median and the mode for each list of numbers
32,35,36,44,46,46,59
Q2. Find the range and standard deviation for each distribution
14,17,18,19,32
Q3. A machine that fills quart orange juice cartons is set to fill them with 32.1oz. If the actual contents of the cartons vary normally, with a standard deviation of .1oz what percent of the cartons contain less than a quart (32oz)?
Q4. White flies are devastating california crops. An area infested with white flies is to be sprayed with a chemical which is known to be 98% effective for each application. Assume a sample of 1000 flies is checked. Find the approximate probability that exactly 980 of the flies are killed in one application.
Q5. The average resident of a certain east coast suburb spends 42 minutes per day communting, with a standard deviation of 12 minutes. Assume a normal distribution. Find the percent of all residents of this suburb who have the following commuting times; No more than 35 minutes per day
Q6. A survey was given to 313 performers appearing in 23 broadway companies. The percentage of performers injured during pracitice or a performance was 55.5%. If a random sample of 500 broadway preformers is taken use the normal approxmation to the binomial distribution to find the approixmate probability that more than 300 preformers have been injured.
Provide complete and step by step solution for the question and show calculations and use formulas.