Extra Credit Assignment of MATH 1680 (Fall011):- Instructor: Koshal Dahal A Perfect assignment is worth 5 else is 0. A Hard Copy of complete (details & organized) solutions of this Assignment must be turned in by December 6 to get the FULL credit. The selected answer key is at the back for your reference. Note that you are FREE to use any help-lines from any sources, excluding me, to do this assignment. Write your name (Last/First), UNT-ID number and Section number, clearly at the top of your answer sheet and staple it!! Chapter 3 Q.2. In a college statistics class, the final exam scores were distributed as follows: Score Count 0-10 5 10-50 8 50-60 0 60-70 7 70-80 15 80-90 24 90-100 22 Assume that for each class interval, the left end point falls in that class interval. a) Draw a relative frequency histogram for the data. b) If it took an 80% to make a B on the final, what percentage of the class made B s or better?
Q.8. A histogram representing the distribution of SAT scores for students in a certain high school is shown below. a) About what percentage of students scored above 1350 on the SAT? b) About half the students did better than what score? c) Did more students score above 1500 or below 800? Chapter 4 Q.2. Calculate a) the median, b) the average, and c) the standard deviation of {-1, 2, 4, 5, 6, 10} Q.7. In a college statistics course, the average score among 20 students who took the first exam was 70%. A few days later, one student took a make-up exam, and she scored a 90%. What is the new average for the class? Q.9. (Hypothetical) the number of years to graduate for students at a certain university is 5 on average, with an SD of 1.5 years. a) About what proportion of the students will graduate between 3.5 and 6.5 years? b) If you picked a student at random, the chance that they will graduate between 3.5 and 6.5 years is about.
Q.10. In one state, the price of gas last year was $2.57/gallon on average, with an SD of $0.20/gallon. For the next year, the legislature imposes a 10% tax on gas. Assuming that the next year s gas prices will be like last year s, what effect will the tax have on the average and SD of gas prices? Chapter 5 Q.8. Attendance for a high school s football games is approximately normal, with an average attendance per game of 1,000 fans and an SD of 200. If the school charges $10 per ticket, about what percentage of the time does the school have a revenue of more than $12,500? Q.9. The times that the city bus arrives at a certain apartment complex each morning are approximately normally distributed, with an average time of 7:30 AM and a standard deviation of 10 minutes. 7:35? 7:45? a) About what percentage of the time will the bus arrive between 7:25 and b) About what percentage of the time will the bus arrive between 7:15 and Chapter 8 c) If you want to have a 95% certainty that you will catch the bus (that is, you arrive before the bus does), what time should you arrive at the stop? d) 90% of the time, the bus will arrive no later than. Q.2. Given the following information on women s heights and weights in a class, sketch a scatter plot. (Hint: This can be done by first plotting the point of averages, then using the SD s and the correlation coefficient to draw the appropriate oval around the point of averages.) Average Height = 65 inches SD of Height = 3 inches Average Weight = 125 pounds SD of weight = 10 pounds r = 0.45
Q.7. Calculate the correlation coefficient, r, to two significant figures. X 1 3 4 5 7 Y 5 1 4 3 7 Chapter 9 Consider the pairs of data sets given below, which have the given five statistic summaries. A B C D 1 5 2 8 3 1 4 7 4 4 6 6 5 3 8 5 7 7 5 4 A Average: 4 A SD: 2 C Average: 5 C SD: 2 B Average: 4 B SD: 2 D Average: 6 D SD: 1.414 r = 0.400 r = -0.707 Then compare the pair of data sets with the above pairs, looking for changes of scale. State the changes and the new five statistic summary based on that change. Q.4) X 4 10 16 22 13 Y 19 17 15 13 11
Q.6. a) Calculate the five statistic summary for the following pair of data sets: X 10 30 40 50 70 Y 9 1 7 5 13 b) Add the point (100, 0) to the list from a). What is the new five statistic summary? Did adding just this one point make a lot of difference? Chapter 10 Q.1. Use the following information for students in a certain class. Average weight: 150 pounds Average height: 68 inches SD for weight: 20 pounds SD for height: 2.5 inches Correlation (r): 0.6 a) Write the regression equation for weight on height (that is, the line that estimates weight when height is given). b) Use the equation to estimate the average weight of students who are 64 inches tall. c) If we randomly select a student and find she is 64 inches tall, what weight should we predict her to have? Q.6. Use the following information from a study on fuel efficiency in sedans. Average age: 6 years SD of age: 2 years Average fuel efficiency: 30 mpg (miles per gallon) SD on efficiency: 4 mpg Correlation (r): -0.84
a) Predict the fuel efficiency of a 10-year old sedan. b) Predict the age of a sedan which gets 20 miles to the gallon. c) If a sedan was chosen at random and you were told nothing about its age, what would be your best prediction on its fuel efficiency? Q.8. Use the following information from an early-season track practice in which 100 runners were timed for two successive mile runs. Average 1 st mile time: 5:20 Average 2 nd mile time: 5:20 SD on 1 st mile: 0:08 SD on 2 nd mile: 0:12 Correlation (r): 0.35 a) Predict the 2 nd mile time for a runner who ran the 1 st mile in 5:47. b) Predict the 2 nd mile time for a runner who ran the 1 st mile in 5:15. Chapter 11 Q. 5. {Under the given information as in Q.6 of above chap. 10} a) Predict the fuel efficiency of a 10-year old sedan, and give the RMS error for your prediction. b) Approximately what percentage of 10 year old sedans should get better than 25 mpg? Q.9. Use the following information on temperature and gas prices in 2006 (the correlation is hypothetical). Average temperature: 65.4 Average cost of gas: $2.50/gallon SD for temperature: 14.5 SD for gas price: $0.29/gallon Correlation (r): 0.65
a) Predict the price of gas when the temperature is 80, and give the RMS error or your prediction. b) Predict the temperature for the day if you read in the paper that gas prices are $2.10 per gallon, and give the RMS error for your prediction. Chapter 13 Q.2. Three cards are dealt off the top of a well-shuffled standard deck of cards. a) What is the probability that the first card is a heart? b) Given that the first card is a heart, what is the probability that the second card is a spade? c) Given that the first was a heart and the second is a spade, what is the probability that the third is another heart? d) What is the probability that the first card is a heart, the second card is a spade, and the third card is a heart? Q.4. Each time a shopper buys toothpaste, he chooses either Brand X or Brand Y. Suppose that, for the first month, he flips a fair coin to decide whether to buy Brand X or Brand Y. Also, for each purchase after the first, he sticks with the same brand next month with probability 3/5, and he switches with probability 2/5. What is the probability that his first and second purchases will be Brand X and his third and fourth purchases will be Brand Y? Q.6. Suppose that for a particular archer practicing her skills, the probability that her arrow hits the bullseye is 0.6. She shoots four arrows in her practice. a) What is the probability that all four arrows miss the bullseye? b) What is the probability that at least one will hit the bullseye? Q.8. In the game of BINGO, there are 60 balls marked with letters and numbers. The balls marked with a B have numbers 1-12, those with an I have numbers 13-24, and so on. The balls are drawn randomly without replacement.
a) What is the probability that the first ball drawn has a G on it? b) What is the probability that the first ball drawn has an even number on it? c) Are the events in a) and b) independent? Why or why not? Chapter 14 Q.4. Suppose you draw one card from a well-shuffled standard deck. a) What is the probability that you draw a face card? (A face card is a Jack, Queen, or King from any suit) b) What is the probability that you draw a diamond? c) What is the probability that you draw both a face card and a diamond? d) What is the probability that you draw either a face card or a diamond? Q.6. We play a game where you roll a die and I roll another die. You win if your die is higher than mine, and you lose otherwise. a) What is the probability that you win the game? b) If I roll first and get a 5, what is your probability of winning now? c) If I roll first and get a 2, what is your probability of winning now? Q.8. You throw a pair of fair 6-sided dice. What is the probability that at least one of the dice shows a 4? Chapter 15 Q.2. You flip a fair coin 10 times. a) What is the probability of getting exactly 5 heads? b) What is the probability of getting 4 to 6 heads inclusive (i.e., getting 4 or 5 or 6 Heads)?
Q.3. Now you flip a weighted coin 10 times. The coin is weighted so that the probability of getting heads is 9/10. a) What is the probability of getting 8 heads? b) What is the probability of getting an even number of heads? c) What is the probability of getting an odd number of heads? Q.8. Suppose that for a particular archer practicing her skills, the probability that her arrow hits the bullseye is 0.7. She shoots ten arrows in her practice. a) How many arrows should she expect to hit the bullseye with? b) What is the probability exactly 7 of them will hit the bullseye? c) What is the probability that more than 7 will hit the bullseye? d) What is the probability that fewer than 7 will hit the bullseye? Chapter 16 Q.9. Suppose you draw from the box 1 2 3 4 5 6 7 a total of 70 times. a) What is the largest value the sum total can be? The smallest? b) What is the average of the box? c) What might you expect the sum to be? Q.10. If five draws are made from the box 1 2 4 6 8, what is the probability that you draw all even numbers: a) If the draws are made without replacement? b) If the draws are made with replacement? Chapter 17 Q.4. Suppose you count the number of aces on 900 rolls of a fair 6-sided die.
a) How many aces do you expect to get, and how far are you likely to be off? b) Suppose I say that for a $1 bet, you will net $4 if you roll an ace and lose your $1 if you don t roll an ace. How much to you expect to win (or lose) in 900 bets, and how far are you likely to be off? Q.5. I offer you the following game: we each roll a die, and if you get strictly more than me on your roll, you win $1. Otherwise, you lose $1. a) What is the expected value for this game for you? Is the game fair? b) Suppose I change the rules so that if we tie, you get your dollar back but don t win anything. Now what is your expected value? Q.6. In the following game, you and I each flip two coins. You win if you have more heads than me; I win otherwise. If a loss costs you $5, how much should you gain each time you win in order to make the game fair? Q.10. Suppose you play roulette a number of times, each time betting $1 on red (recall that there are 18 slots on a roulette wheel and a bet on red pays 1 to 1). Complete the following chart showing the expected value and standard error as you play n times. N EV n SEn 1 10 100 1000 10000 Chapter 18 Q.1. Suppose you flip a fair coin 50 times. a) Estimate the probability that fewer than 23 heads are flipped. b) Estimate the probability that 23 to 27 heads (inclusive) are flipped.
Q.5. Suppose you roll a pair of fair 6-sided dice 36 times. a) What is the exact probability of getting six 7 s? b) Use the Central Limit Theorem to approximate the probability of getting six 7 s. (Hint: What range do you need to use on the normal curve to represent 7 to the nearest integer?) Q.8. You play a game where you draw from a well-shuffled standard deck of cards. If you draw a face card (Jack, Queen, or King), you win $3. Otherwise, you lose $1. If you played this game 100 times, what is the probability that you would lose more than $15? Chapter 20 Q.1. In a population of 10,000 people of which 5,000 are men, complete the chart giving the standard error for the percentage of men, both with and without the correction factor, for the given sample sizes. n SE(P) (with correction factor) SE(P) (No correction factor) 100 900 1,000 6,400 Q.3. Consider drawing from the given box containing 2,500 tickets, all 0 s and 1 s. Draw the specified number of time from 400 tickets from 0 x 1,175 1 x 1,325, with replacement. a) What percentage of your sample do you expect to be 1 s? How far off are you likely to be?
b) What percentage of your sample do you expect to be 0 s? How far off are you likely to be? c) Can you use the normal curve to estimate the probability that you get more than 52% 1 s? If so, then estimate it. If not, explain why not. Q.5. 1600 tickets from 0 x 1,370 1 x 1,130, without replacement. a) What percentage of your sample do you expect to be 1 s? How far off are you likely to be? b) What percentage of your sample do you expect to be 0 s? How far off are you likely to be? Q.8. According to the 2000 US Census, of Americans 25 years or older, 80.4% are high school graduates and 24.4% have at least a Bachelor s degree. There were about 281 million Americans in 2000. a) If one was to take a simple random sample of 900 Americans age 25 or more, what is the probability that the sample would contain less than 79% high school graduates? b) What is the probability that the sample would contain between 23% and 26% college graduates? Chapter 21 Consider taking a sample of the given size from a box containing 50,000 tickets, all 0 s and 1 s. Q.2. A sample of 80 tickets has 47% 1 s. a) What percentage of the entire box do you expect to be 1 s? What is the standard error on your estimate? b) Can you give a meaningful 99.7% confidence interval for the percentage of 1 s in the box? If so, then estimate it. If not, explain why not.
Q.9. A pizza restaurant wants to determine whether to open a store in a college town. He needs to have at least 15% of the town eat at the restaurant to justify the expense of opening. In order to check this, the owner surveys 100 residents and finds that 19 of them would eat pizza from his restaurant. Find a 95% confidence interval for the percentage of the town s population that would do business with the restaurant. Should the owner open the restaurant? Chapter 23 Q.2. A sample of 80 tickets has an average of 12.6 and an SD of 4. a) What should you estimate the average of the entire box do to be? What is the standard error on your estimate? b) Can you give a meaningful 68% confidence interval for the average value in the box? If so, then estimate it. If not, explain why not. Q.6. (Hypothetical) Out of 30,000 students enrolled at a university, 400 students are chosen at random. The average age of the students sampled is 21.7 years; with an SD is 6.5 years. a) Estimate the average age and standard error for all 30,000 students. b) Can you give a meaningful 95% confidence interval for the average age of all students? If so, give the interval. If not, explain why not. Chapter 26 Q.2. A gambler goes to the local casino and observes the action at the craps table for 400 throws of the dice. He finds that 80 of the throws come up 7. State the null and alternative hypotheses, and find the P-value of his observations. Is this a statistically significant result?
SELECTED ANSWER KEY:- Chapter 4: 10) the new average will be $2.83/gallon with an SD of $0.22/gallon. Chapter 5: 8) 10.565% 9 c) Around halfway between 7:13 AM and 7:14 AM Chapter 10: 1 b) 130.8 pounds Chapter 11: 5. b) About 21% 9.b) $(2.69 ± 0.22)/gallon Chapter 13: 4) 7.2% 8. c) Yes, show P(G & Even) = P(G)P(Even). The End!!