403 Math Practice Exam 2
1. A bag contains five blue balls and three red balls. A boy draws a ball, and then draws another ball, without putting back the first. What is the probability that he draws 2 red balls?
2. Suppose 2 of the next 12 persons entering a bar are underage. If a police officer randomly selects 3 of the next 12 persons entering the bar, what is the probability the he selects neither of the underage persons?
3. If 30% of all car accidents are due to distracted drivers, what is the probability that of the next 20 accidents 2 are due to distracted driving?
4. A starter motor utilized in a space vehicle possesses a high reliability and is reputed to start on any given occasion with probability .99999. If the starts are considered independent, what is the probability of at least one failure in the next 10,000 starts?
5. The number of complaints, which a dry-cleaning establishment receives per day, is a random variable having a Poisson distribution with an average of 3.3. a. What is the probability that the number of complaints received on a particular day is less than two?
b. What is the probability that the number of complaints received over 4 days is equal to 10?
6. If an expert sharpshooter misses a target 5% of the time find the probability that she will miss the target: a. For the second time on the fifteenth shot.
b. Three times out of 10.
c. Three times out of 10 for the first time on the third day of practice (assuming she tries 10 times each day).
7. The number of people entering the intensive care unit at a particular hospital on any one day possesses a Poisson distribution with a mean equal to 5 persons per day. What is the probability that the number of people entering the intensive unit care on a particular day is equal to two?
8.
The finished inside diameter of a washer has an average of 0.25 inches. If these diameters tend to follow a normal distribution with a standard deviation of 0.002 inches, find the following. a) The probability that a randomly selected washer has a diameter of 0.2524 or less.
b) The probability that a randomly selected washer has a diameter of between 0.251 and 0.2561.
c) The diameter such that only 3% of all washers have a diameter that is larger.
9. The number of telemarketing calls received by a residence follows a Poisson distribution. A residence receives, on average, 7 telemarketing calls per week. What is the probability that it will take less than 5 days for the first call?
10. The lifetimes of a certain automobile seal follow a Weibull distribution with = 1/8 and =1/3. a) What is the average expected lifetime of this seal?
b) What is the probability that one of these seals will last less than 8 years?
11. Suppose that the number of trumpeter swans in a migrating flock has approximately a normal distribution with a mean or 11.6 and a standard deviation of 4.0. Find the probability that such a flock contains at least 17 birds.
12. Repair time for an oil change at a car dealership has a population mean of 40 minutes and a population standard deviation of 5 minutes. If a random sample of 100 oil changes is selected, a) What is the probability that the sample mean is above 38.5 minutes?
b) There is a 95% chance that the sample mean is above which value?
Answers: 1. .1071 2. .5454 3. .0278 4. .095163 5. a) .1586 b) .0819 6. a) .01797 b) .0105 c) .01028
7. .0842 8. a) .8849 b) .3074 c) .25376 9. .99326 10 a) 48 b) .632 11. .0885 12. a).9987 b) 39.18