ductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.PD.DRV.01.0020A [1 mark] mark] Select the random variable that is discrete: A number is assigned equal to the length of time a caller must wait on hold before they receive customer assistance from their bank. If a computer program takes longer than 10 seconds to compile, the value 1 is assigned. If it takes less than 10 seconds, the value 0 is assigned. The percentage increase or decrease in volume of an amount of liquid is assigned after that liquid is treated to a chemical reaction. After 10 athletes throw a javelin, the longest distance thrown is recorded. 2 of 3 ID: MST.FET.PD.DRV.02.0040A [12 marks] marks] Geoff is running a carnival game. He has 15 marbles in a bag: there are 4 green marbles, 7 red marbles and 4 yellow marbles. To play a round of the game, a player randomly takes out a marble from the bag, notes the color and replaces it, then pulls a second marble from the bag and notes the color. So in effect, the player pulls 2 marbles from the bag. (However, the first marble is put back in the bag and so potentially could be pulled twice.) Green marbles win 5 points, red marbles win 2 point and yellow marbles lose 2 points. Let X be the random variable that describes the number of points won by a player playing a single round of Geoff's marble game. Find the probability distribution for X. Give values for X as whole numbers and probabilities as decimal values to 3 decimal places. Enter the values for X in ascending order (lowest to highest) from left to right in the table. X P(X = x) 3 of 3 ID: MST.FET.PD.DRV.03.0010A [2 marks] marks] Suppose Y is a discrete random variable with probability distribution given by: P(Y = k) = k/21 , for k = 1, 2, 3, 4, 5, 6 a) Calculate the expected value of Y. Give your answer to 2 decimal places. E[Y] = b) Calculate the variance of Y. Give your answer as a decimal to 2 decimal places. VAR[Y] = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Sunday, April 24, 2016, 15:20 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.PD.BD.01.0010A [1 mark] mark] An analyst has been studying a particular stock and has come to the following two conclusions: the probability that the stock will rise on a particular day is 0.3 the rise or fall of the stock on any particular day is independent of the rise and fall of the stock on any other day Calculate the probability that over the next week (7 days) the stock will rise on exactly 4 days. Give your answer as a decimal to 2 decimal places. Probability = 2 of 3 ID: MST.FET.PD.BD.02.0020A [1 mark] mark] You are a day trader on the stock exchange and you have invested all of your life savings in a portfolio containing 6 stocks. After dwelling on the risks involved in your investment, you have come to the conclusion that if at most half of the stocks in your portfolio are profitable, your investment will be a failure. Based on empirical data available from the historical records of the stock exchange, you believe that the probability of a stock being profitable is 0.4. Assuming that the profitability of each stock is independent of all the other stocks, calculate the probability (P(F)) that your investment is a failure. Give your answer as a decimal to 2 decimal places. P(F) = 3 of 3 ID: MST.FET.PD.BD.03.0030A [1 mark] mark] Ken is a factory worker, who is a part-time statistics student, and makes toys. He knows that the probability that any given toy on the factory line is faulty is a constant and is independent of whether or not any other toy on the line is faulty. Through testing, Ken concludes that if a sample of 70 toys are inspected, the expected number of faulty toys will be 3. Calculate the probability that a randomly chosen toy is faulty. Give your answer as a decimal to 2 decimal places. Probability that a toy is faulty = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Sunday, April 24, 2016, 15:20 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 1 ID: MST.FET.PD.CRV.01.0030A [1 mark] mark] A student provides four conditions that a function must satisfy in order to be a probability density function. However, only one of the conditions is actually correct. Of the following four statements, the one that accurately describes a property that a function must possess in order to be a probability density function is: The set of values along the horizontal axis that the function assigns values to must be the set of values between 0 and 1. The function must not go below the horizontal axis at any point. The area between the function and the horizontal axis must be less than or equal to 1. The function must not take values greater than 1. Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Sunday, April 24, 2016, 15:21 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.PD.ND.01.0040A [2 marks] marks] Let X be a normal random variable with a mean of -3.14 and a standard deviation of 3.04. a) The z-score that corresponds to a particular data point (x) is 0.71. Calculate the data point. Give your answer to 2 decimal places. x= b) The area under the standard normal probability density function from 0.71 to infinity is interpreted as the probability that X is: less than or equal to x equal to x greater than or equal to x 2 of 3 ID: MST.FET.PD.ND.02.0020A [2 marks] marks] American Expresso sells coffee and assorted pastries. A manager at a particular coffee stand has noticed that muffins contribute a substantial amount to the costs of running that stand. She wants to make sure that the stand is selling enough muffins to justify their continued existence at the stand. Ideally, the manager would like to sell at least 120 muffins each day. Some research has shown that the average number of muffins sold each day is 144, and the standard deviation in the number of muffins sold is 21. You may find this standard normal table useful throughout the following questions. a) Calculate the percentage of days on which the coffee stand sells less than the ideal number of muffins. Give your answer as a percentage to 1 decimal place. Percentage of 'failure' days = % b) The manager would like to have no more than 2.5% of days being failures. However, at the moment the manager can't do anything about the average number of muffins sold and the standard deviaiton in muffins sold. Her only option is to try and lower costs, to change the limit of what is considered a 'failure'. Calculate the number x such that the following statement is true: 'The coffee stand sells less than x muffins on 2.5% of days or less.' x= 3 of 3 ID: MST.FET.PD.ND.03.0010A Sam 'Vandelay' Johnson plays basketball for his college team. You've observed that the probability of Sam making a given shot is 0.55 and that the success of a given shot is independent of other shots. Over the course of many games, Sam takes 100 attempted shots at the basket. Let W be the random variable that is the number of successful shots. [3 marks] marks] You should use the normal approximation to the binomial to calculate the probabilities in parts b) and c). Give your answers as decimals to 4 decimal places. a) Find the probability that Sam makes exactly 56 successful shots from the 100 attempts. P(W = 56) = b) Find the probability that Sam makes at most 56 successful shots from the 100 attempts. P(W 56) = c) Find the probability that Sam makes between 50 and 60 successful shots from the 100 attempts. P(50 W 60) = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Sunday, April 24, 2016, 15:21 http://www.perdisco.com.au Part 1 1. The value of this variable is only 0 and 1 For the test of the answers it is measure of time and hence it is continuous 2. Combinations Amount Probabilty 0.071 2 7*4 56 15 * 15 225 0.249 2 RR 4*4 16 15 * 15 225 7*4 56 15 * 15 225 0.249 4*4 16 15 * 15 225 0.071 4*4 32 15 * 15 225 0.142 7*7 49 15 * 15 225 0.218 4 RG 7 RY 0 YY -4 2* YG 3 GG 10 The solution is X P(x) 3. -4 0.071 0 0.249 3 0.142 4 0.071 7 0.249 10 0.218 12 2 2 3 2 4 2 5 2 6 2 E (Y ) YP( y ) 4.33 21 Var (Y ) E (Y 2 ) E (Y ) 2 13 2 3 33 4 3 5 3 6 3 4.332 2.22 21 The solution is E(Y)=4.33 Var(Y)=2.22 Part 2 1. X Number of days the stock will rise X ~ B(7,0.3) P(X 4) 7C 4 0.3 4 0.7 3 0.09724 ~ 0.10 The solution is 0.10 2. X number of stocks that are profitable X ~ B(6,0.4) 3 P(X 3) 6C x 0.4 x 0.6 6 x 0.82 x 0 The answer is 0.82 3. n 70 E ( x) np 2 70 p 2 2 p 0.03 70 The answer is 0.03 Part 3 1. This means that probability cannot be 1 Part 4 1. x Z 0.71 3.04 3.14 -0.9816 The answer is -0.98 b. 2. X ~ N (144,21) P( X 120) 0.12655 Use excel function normdist(120,144,21,1) The answer is 12.7% P( X a) 0.025 a 102.84 used excel function norminv(0.025,144,21) The answer is 102.84 . If it has to be rounded up then the answer is 103 3. a. P( w 56) 100C 56 0.5556 0.4544 0.0786.Use d excel function binomdist(56,100,0.55,0) b. P( w 56) mean np 55 stdev 100 * 0.55 * 0.45 4.975 P(w 56) 0.5797. Used excel function normdist(56,55,4.975,1) c. P(50 w 60) normdist(60,55,4.975,1) - normdist(50,55,4.975,1) 0.6851 The answers are a. 0.00786 b. 0.5797 c. 0.6851