Name:______STAT 50
Date: 3/10/2011 Quiz 3
A formula you may need:
1. (8 points) A bag contains 8 scrabble letters. The letters in the bag are:
E1 K5 J8 Q10 P3 C3 G2 I1
The procedure is to draw a single letter from the bag without looking in the bag. The number next to each letter tells you how many points each letter is worth. Let be the event that a vowel is drawn and let be the event that a letter worth 5 or more points is drawn. Find
a) b) c) d)
e) f) c) d)
2. (1 point) In order for the weatherman to determine if it is going to rain today, he looked at past records and noticed that out of 1287 days in the past that had all the same conditions as today has, it has rained on 821 of those days. What is the probability that it rains today?
3. (1 point) If denotes the sample space of a procedure, what is Why?
Name:______STAT 50
Date: 3/15/2011 Quiz 4
Some formulas you may need:
1. (2 points) Consider the procedure where you draw a single card from a standard poker deck. Let be the event that you draw a diamond and let be the event that you draw a 7. Find the probability that you draw a diamond or a 7.
2. (4 points) Suppose a bag contains 5 red balls, 3 green balls and 2 yellow balls. Consider the procedure that you draw 2 balls from this bag one at a time without replacement. Find
a) The probability that you draw a green ball first and then a yellow ball
b) The probability that you draw a red ball both times
3. (2 points) Consider the procedure where you draw 2 cards from a standard poker deck without replacement. Find the probability that you get at least one ace.
4. (2 points) Consider the procedure where you spin the spinner below once. Let be the even that the spinner lands on a red number and let be the event that the spinner lands on an even number.
a) Are the events and disjoint? Why or why not?
b) Are the events and independent? Why or why not?
Name:______STAT 50
Date: 3/17/2011 Quiz 5
1. (2 points) How many 7 character license plates are there where the 2nd, 3rd and 4th characters are letters (A-Z), the rest of the characters are numbers (0-9), and no letter can be used more than once (but the numbers can repeat).
2. (2 points) How many (distinguishable) permutations are there of the word BANANA?
3, (2 points) Out of a senior class of 20 students, 4 people are going to be picked to be on the yearbook committee. How many different committee choices are possible?
4. (2 points) In horse racing, betting an exacta means picking which horse will come in first and which will come in second in the correct order. How many different exacta bets are possible in a 12 horse race?
5. (2 points) You have 5 books that you are going to arrange on a shelf. How many different arrangements are possible?
Name:______STAT 50
Date: 3/22/2011 Quiz 6
Formulas you may need:
1. (2, 2, 2, 1 points) Suppose you are betting on the draw of a single card from a standard poker deck. You will win $5 if you draw a heart, win $2 is you draw a spade, and lose $4 if you draw anything else. Let X stand for the amount of money you will win when making this bet once.
a) Find the probability distribution of X
b) Find the mean of X
c) Find the standard deviation of X
d) What is the meaning of the mean of X?
2. (3 points) You have a bag with 4 green balls, 2 red balls and 1 yellow ball in it. You draw 15 balls from this bag one at a time with replacement. What is the probability that you draw a yellow ball exactly 3 times?
Name:______STAT 50
Date: 4/05/2011 Quiz 7A,B
1. (1, 1, 1, 2, 2, 2, 1 points) Suppose Z has a standard normal distribution.
a) What are the possible values for Z?
b) What is the mean of Z?
c) What is the standard deviation of Z?
d) What is
e) What is
f) What is
g) What is
2. (2 points) State the requirements for a density curve.
3. (2 points) Suppose X is a random variable with the density curve drawn below.
a) What are the possible values of X?
b) What is ?
4. (2 points) Suppose X is uniformly distributed over the interval [3,13].
a) Find c that makes this a probability density.
b) Find
5. (4 points) Suppose the heights of 40 year old males is normally distributed with a mean of 70 inches and a standard deviation of 6 inches. What is the probability that a randomly selected 40 year old man’s height is between 64 inches and 76 inches? (Hint: Let X denote the height of a 40 year old male)
Name:______STAT 50
Date: 4/07/2011 Quiz 8
Some formulas you may need:
1. (1, 2 points) Let X be the number face up on a die if a die is rolled once. Let be the average of the face up numbers on the die if the die is rolled twice. Find
a) b)
2. (3 points) The Doritos chip company claims that the number of chips in their small bags of Doritos has a mean of 20 chips and a standard deviation of 2 chips. What is the probability that the average number of chips in a sample of 64 bags of chips is less than 19.5 chips.
3. (4 points) IQ scores of 18 year olds are normally distributed with a mean of 130 points with a standard deviation of 5 points. Find
a) the probability that if one 18 year old is randomly selected, his or her IQ score will be more than 132 points.
b) the probability that if nine 18 year olds are randomly selected, their average IQ score will be more than 132 points.
Name:______STAT 50
Date: 4/12/2011 Quiz 9
Some formulas you may need:
Make sure to answer the question below showing all work I have asked you to show for such problems in class.
1. (10 points) A Boeing 767-300 aircraft has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). A ticket agent accepts 236 reservations for a flight that uses a Boeing 767-300. Find the probability that not enough seats will be available. Is this probability low enough so that overbooking is not a real concern?
Name:______STAT 50
Date: 4/14/2011 Quiz 10
Some formulas you may need:
1. (1, 3, 2 points) PCC is considering putting energy drink vending machines on campus. Before they decide, the president of PCC wants to know what percentage of PCC students drink energy drinks on a regular basis. To figure this out, the president asks his favorite statistics professor Greg Miller to poll his stats class and get an estimate. Of the 35 students in Greg’s stats class, 7 say that they drink energy drinks on a regular basis.
a) What is the best point estimate for the percentage of all PCC students who drink energy drinks on a regular basis?
b) Find a 95% confidence interval for the percentage of all PCC students who drink energy drinks on a regular basis.
c) What does the 95% in a 95% confidence interval mean?
2. (1, 3 points) To estimate the average amount of money that people take when they go to a casino, Morongo asked 100 of its visitors how much money they brought with them to the casino. The average amount of money that these 100 people brought with them was $130. Assume that the standard deviation of the amount of money that all casino visitors bring with them to the casino is $22 and assume that those who were polled told the truth.
a) What is the best point estimate for the average amount of money that casino goers bring with them to the casino?
b) Find an 88% confidence interval for the average amount of money casino goers bring with them to the casino
Name:______STAT 50
Date: 5/02/2011 Quiz 11
A formula you may need:
1. (5 points) Cheating Gas Pumps When testing gas pumps in Michigan for accuracy, fuel-quality enforcement specialists tested pumps and found that 1299 of them were not pumping accurately (accurately means within 3.3 oz when 5 gallons are pumped), and 5686 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of Michigan gas pumps are inaccurate.
2. (5 points) Driving and Cell Phones In a survey, 1640 out of 2246 randomly selected adults in the United States said that they use cell phones while driving. Use a 0.05 significance level to test the claim that the proportion of adults who use cell phones while driving is equal to 75%.
Name:______STAT 50
Date: 5/05/2011 Quiz 12
Some formulas you may need:
1. (5 points) Weights of Pennies The U.S. mint has a specification that pennies have a mean weight of 2.5 g. A simple random sample of 37 pennies manufactured after 1983 was taken and those pennies have a mean weight of 2.49910 g and a standard deviation of 0.01648 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g.
2. (5 points) The Doritos company claims that the average number of chips in their small bags of chips is 20 chips. A disgruntled consumer claims that Doritos is cheating their customers and are putting less chips in their bags than they should. To this end, a sample of 49 bags of chips is obtained and the average number of chips in this sample is 18.3 chips. Suppose that the standard deviation of the number of chips in all Doritos bags is 3.5 chips. Use a 0.01 significance level to test the claim that the mean number of chips in small Doritos bags is less than 20 chips.
Extra Credit (5 points): Suppose you have data that is normally distributed with and .
a) 68% of the data will be between what two numbers?
b) What percent of the data will be between the numbers 18 and 46?
c) 99.7% of the data will be between what two numbers?
Name:______STAT 50
Date: 5/10/2011 Quiz 13
Some formulas you may need:
1. (10 points) A can of Coke is supposed to contain 12 oz’s of soda. However, the amount of soda in each can will vary somewhat. The Coca-Cola company claims that the standard deviation of the amount of soda in their cans is 0.15 oz’s. To make sure that the amount of soda in each can is consistent and that their machines used to fill the cans are working properly, an inspector measures the amount of soda in 49 cans and finds that the standard deviation of the sample is 0.21 ounces. Test the claim that the standard deviation of the amount of soda in a can of Coke is larger than 0.15 oz’s at the 0.05 significance level. Is the Coca-Cola company lying? Do their filling machines need upgrading?
Name:______STAT 50
Date: 5/12/2011 Quiz 14
Some formulas you may need:
1. (5 points) Adverse Effects of Viagra In an experiment, 16% of 734 subjects treated with Viagra experienced headaches. In the same experiment, 4% of 725 subjects given a placebo experienced headaches. Use a 0.01 significance level to test the claim that the proportion of headaches is greater for those treated with Viagra. Do headaches appear to be a concern for those who take Viagra?
2. (5 points) Adverse Effects of Viagra Using the sample data from problem 1, construct the confidence interval corresponding to the hypothesis test conducted with a 0.01 significance level. What conclusion does the confidence interval suggest?
Name:______STAT 50
Date: 5/24/2011 Quiz 15
Some formulas you may need:
1. (5, 5) The data below are blood pressure measurements of 5 patients taken once from their left arms and once from their right arms. Use x to denote a patient’s right arm blood pressure and let y denote a patient’s left arm blood pressure.
Right Arm x / 102 / 101 / 94 / 79 / 79Left Arm y / 175 / 169 / 182 / 146 / 144
a) Find r
b) Find the least squares regression line for the data
Extra Credit (5, 5 points)
a) Use the least squares regression line to predict a patient’s blood pressure in their left arm if the blood pressure in their right arm is 100 mm Hg.
b) Use the least squares regression line to predict a patient’s blood pressure in their right arm if the blood pressure in their left arm is 200 mm Hg.
Name:______STAT 50
Date: 5/26/2011 Quiz 16
1. (5 points) In order to study global warming, the data below was taken over different years (CO2 levels in parts per million and temperature in ).
CO2 x / 314 / 317 / 320 / 326 / 331 / 339 / 346 / 354 / 361 / 369Temperature y / 13.9 / 14 / 13.9 / 14.1 / 14 / 14.3 / 14.1 / 14.5 / 14.5 / 14.4
After doing all the regression calculations, the equation of the least squares regression line for this data is . Construct a 95% prediction interval that predicts what the temperature of the Earth will be if the CO2 level reaches 400 parts per million.
2. (5 points) The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby?
Post Position / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Wins / 19 / 14 / 11 / 14 / 14 / 7 / 8 / 11 / 5 / 11
Some formulas you may need:
Name:______STAT 50
Date: 5/31/2011 Quiz 17
Some formulas you may need:
1. (10 points) Which Treatment Is Better? A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below. The results are based on evaluations made one year after the treatment. Using a 0.01 significance level, test the claim that success is independent of the type of treatment. What do the results suggest about treating carpal tunnel syndrome?
Successful Treatment / Unsuccessful TreatmentSplint Treatment / 60 / 23
Surgery Treatment / 67 / 6
Name:______STAT 50
Date: 3/03/2011 Exam 1
Please show ALL your work on the problems below. No more than 1 point will be given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
1. (7, 7, 7, 7, 7, 13, 7 points) Consider the data below:
Data = 5, 8, 9, 9, 12, 14, 22, 12, 8, 8
a) Find the mean of the data
b) Find the median of the data
c) Find the mode(s) of the data
d) Find the midrange of the data
(this is a continuation of question 1)
e) Find the range of the data
f) Find the standard deviation of the data
g) Find the variance of the data
2. (20, 7, 10 points) Consider the data below:
Data = 10 13 14 18 19 21 27 28 30 44
60 89 101 121 122 184 211 289 327 505
a) Find the 5-number summary for this data
b) Draw a box plot for this data
c) Let denote the standard deviation of the first 10 numbers of the data and let denote the standard deviation of the last 10 numbers of the data. Without calculating or , which one do you think will be bigger? Explain as clearly as possible. (Hint: Look at your box plot in part (b))
3. (24 points) Define and explain the difference between
a) a Population and a Sample
b) a Single Blind and a Double Blind Experiment
c) a Random Sample and a Simple Random Sample
d) Stratified Sampling and Cluster Sampling
4. (24 points) The data below are the ages of the students in my Pre-Algebra class at Valley College:
Data: 30 31 18 36 28 33 32 41 26 34
42 38 21 32 34 31 31 19 25 22
47 25 34 35 37
Use classes of width 5 and start your first class at 15 to
a) Make a frequency table b) Make a relative frequency table
c) Make a relative frequency histogram
d) Is the distribution of this data a Normal Distribution? Explain clearly why or why not.
5. (5 points) What is the main idea of statistics?
6. (5 points) Give an example of a voluntary response sample.
Name:______STAT 50
Date: 3/24/2011 Exam 2
Please show ALL your work on the problems below. No more than 1 point will be given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
1. (51 points) A box contains 8 colored balls with numbers on them as shown below. Consider the procedure where you draw one ball out of the box.
a) What is the sample space? (Hint: To denote an outcome, it is ok to just use numbers)
b) Let be the event that you draw a blue ball and let be the event that you draw an even number. Find the following:
= =
= =
= =
(this is a continuation of problem 1)
c) Find the following probabilities
d) Are the events B and E disjoint? Why or why not?
e) Are the events B and E independent? Why or why not?
2. (8, 8, 8 points)
a) How many 7 character license plates are there where the 2nd, 3rd, and 4th characters are letters (A-Z), the other characters are numbers (0-9) and repetition is allowed?
b) How many 7 character license plates are there where the 2nd, 3rd, and 4th characters are letters (A-Z), the other characters are numbers (0-9) where no number or letter can be repeated?
c) If a 7 character license plate like the ones described in part (a) is chosen at random, what is the probability that no letter or number is repeated?
3. (15 points) At the horse races, betting on an trifecta means that you bet on the which horse comes in 1st, 2nd and 3rd in the correct order. Suppose the race you are betting on has 8 horses and you bet on the 7-2-5 exacta (meaning you are betting that the number 7 horse will come in 1st , the number 2 horse will come in 2nd and the number 5 horse will come in 3rd. Assuming all horses have the same chance of winning, what is the probability that you win your trifecta bet?
4. (5, 15, 5 points) Suppose a gambler is making a bet on the outcome of drawing a single card from a standard poker deck. Specifically, he will win $10 if he draws the Ace of spades, he will win $5 if he draws any other Ace, he will win $3 if he draws any other spade, and will lose $1 if anything else is draws.
a) Find the probability distribution for X.
b) Find the mean, variance and standard deviation of X.
c) Is it in the gambler’s best interest to play this game? Why or why not?
5. (15, 5 points) Suppose a scientist comes up with a drug that he feels cures the common cold. He claims that the probability that his drug will cure a cold is 85%. The scientist administers this drug to 8 people who currently have a cold.