Stat 200 Quiz 2 | Complete Solution

Stat 200 Quiz 2

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1.    (5 pts) A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooden balls. A ball is selected from the bag and kept. You then draw a second ball and keep it also. What is the probability of selecting one white ball and one blue ball? Leave the answer in fractional form.

2.    (5 pts) A student scores 62 on a geography test and 285 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 15. The mathematics test has a mean of 300 and a standard deviation of 10. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class and why?

3.    (5 pts) The probability that Sam parks in a no-parking zone and gets a parking ticket is 10% and the probability that Sam cannot find a legal parking place and has to park in a no-parking zone is 20%.  On Friday Sam arrives at school and parks in a no-parking zone. What is the probability that he’ll get a parking ticket?

4.    (5 pts) The following is a sample of 19 November utility bills (in dollars) from a neighborhood. What is the largest bill in the sample that would not be considered an outlier?

 52, 62, 66, 68, 72, 74, 76, 76, 76, 78, 78, 82, 84, 84, 86, 88, 92, 96, 110

5.    (5 pts) Events A and B are mutually exclusive. If P(A) = 0.7 and P(B) = 0.1, what is P(A and B)?  

6.    (5 pts) If one card is drawn from a standard 52 card playing deck, determine the probability drawing either a jack, a three, a club or a diamond. Leave as a fraction or round to the nearest hundredth.

7.    (5 pts) A human gene carries a certain disease from the mother to the child with a probability rate of 39%. That is, there is a 39% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that at least one of the children get the disease from their mother. Round to the nearest thousandth.

8.    (5 pts) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.99, and P(D) = 0.91. Find the probability that at least one of the four parts will work. Round to six decimal places.

9.    (5 pts) Mamma Temte bakes six pies a day that cost $2 each to produce. On 39% of the days she sells only two pies. On 16% of the days, she sells 4 pies, and on the remaining 45% of the days, she sells all six pies. If Mama Temte sells her pies for $6 each, what is her expected profit for a day's worth of pies? Assume that any leftover pies are given away for free.

10.     (5 pts) A box contains three $1 bills, two $5 bills, five $10 bills, and two $20 bills. Construct a probability distribution for the data if x represents the dollar value of a single bill drawn at random and then replaced.

11.     (5 pts) According to government data, the probability that an adult has never been in a museum is 15%. In a random survey of 10 adults, what is the probability that exactly eight adults have been in a museum?  On average, how many adults of the 10 would we expect to be in a museum?

12.     (5 pts) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 67% regularly use the golf course, 48% regularly use the tennis courts, and 8% use neither of these facilities regularly. What percentage of the 600 uses at least one of the golf or tennis facilities?

13.     (5 pts) The probability that a football game will go into overtime is 15%. What is the probability that two of three football games will go to into overtime?

14.     (5 pts) The tread life of a particular brand of tire is a random variable that is normally distributed with a mean of 60,000 miles and a standard deviation of 2600 miles. What is the probability a particular tire of this brand will last longer than 57,400 miles?

15.     (5 pts) The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.08 ounce. Every can that has more than 12.20 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%?

16.    (5 pts) The amount of corn chips dispensed into a 13-ounce bag by the dispensing machine is a normal distribution with a mean of 13.5 ounces and a standard deviation of 0.1 ounce. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 13.6 ounces.

17.     (5 pts) A cruise director schedules 4 different movies, 2 bridge games, and 3 tennis games in a 2-day period. If a person selects 3 activities, find the probability that he attends 2 movies and 1 tennis game.

18.     (5 pts) A statistics quiz consists of 25 true/false questions. How many different answer keys could be made?

19.     (5 pts) A company’s ID cards consist of 5 letters followed by 2 digits. How many different cards can be made if repetitions are allowed? How many can be made if no repetitions are allowed?

20.     (5 pts) A census indicates that Americans ate an average of 25.7 pounds of confectionary products in one year and spent an average of $61.50 per person doing so. If the standard deviation for consumption is 3.75 pounds and the standard deviation for the amount spent is $5.89, find the probability that for a random sample of 50 Americans, the sample mean for confectionary spending exceeded $60 per person.