problem 1: Suppose 10% of the tubes produced by a machine are defective. If six tubes are inspected at random, determine the probability that:
a) Three tubes are defective.
b) At least two tubes are defective.
c) At most 5 tubes are defective.
problem 2: A box contains a very large number of red, white, blue and yellow marbles in the ratio 4:3:2:1, respectively. Find the probability that in 10 drawings:
a) 4 red, 3 white, 2 blue and 1 yellow marble will be drawn.
b) 8 red, and 2 yellow marbles will be drawn.
problem 3: The suicide rate in a certain state is 1 suicide per 100,000 inhabitants per month. Find the probability that in a city of 400,000 inhabitants within the state there will be 8 or more suicides in a given month.
problem 4: A warehouse receives a shipment of 20 computers, of which 5 are defective. Eight computers are then randomly selected and then delivered to a store.
a) What is the probability that the store receive no defective computer?
b) If the store found out about the defective, what is the probability that it will refuse to pay for the delivery?
problem 5: Consider a roulette wheel consisting of 38 numbers – 1 through 36, 0 and double 0. If Smith always bets the outcome will be one of the numbers 1 through 12, what is the probability that he will lose his first 5 bets? What is the probability that his first win will occur on his 4th bet? What is the probability that his third lose will occur on his fifth bet?
problem 6: Given a normal distribution with µ = 30 and σ = 6. Find
a) The normal curve area to the right of x = 17
b) The normal curve area to the left of x = 22
c) The normal curve area between x = 32 and x = 41
d) The value of x that has 80% of the normal curve area to the left
e) The two values of x that contain the middle 75% of the normal curve area
problem 7: A lawyer commutes daily from his suburban home to his midtown office. The average time for an office trip is 24 minutes with a standard deviation of 3.8 minutes. Assuming that the distribution of trip times to be normally distributed.
a) What is the probability that a trip will take at least 1/2 hour?
b) If the office opens at 9:00 am and leaves his house at 8:45 am daily. What percentage of time is he late for work?
c) If he leaves the house at 8:35 am and coffee is served at the office from 8:50 until 9:00 am, what is the probability that he misses coffee?
problem 8: It is claimed that an automobile is driven on than average more than 20,000 kilometers per year. To test this claim, a random sample of 100 automobile owners is asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deviation of 3,900 kilometers? Use level of significance of 0.05
problem 9: Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance of contents in normal.