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.01.0010A [1 mark] mark] Select the random variable that is not discrete: In a class of 30 students, numbers are assigned to according to the number of students who may pass a test next week. Numbers are assigned according to the length of time it will take to get served at a bank. Numbers are assigned according to the number of days before a share price stops increasing. The number -1 is assigned to a share price falling tomorrow, the number 0 is assigned to the share price remaining stable, and the number 1 is assigned to the share price rising. 2 of 3 ID: MST.FET.PD.DRV.02.0020A [12 marks] marks] Geoff is running a carnival game. He has 14 marbles in a bag: there are 4 green marbles, 6 red marbles and 4 yellow marbles. To play a round of the game, a player randomly takes out 2 marbles (without replacement) from the bag. 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 | Friday, April 29, 2016, 18:43 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.01.0020A [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 0.5 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 number of days that the stock will rise is not 3. Give your answer as a decimal to 2 decimal places. Probability = 2 of 3 ID: MST.FET.PD.BD.02.0010A [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 least half of the stocks in your portfolio are profitable, your investment will be a success. Based on empirical data available from the historical records of the stock exchange, you believe that the probability of a stock being profitable is 0.3. Assuming that the profitability of each stock is independent of all the other stocks, calculate the probability (P(S)) that your investment is a success. Give your answer as a decimal to 2 decimal places. P(S) = 3 of 3 ID: MST.FET.PD.BD.03.0010A [1 mark] mark] Cathy is a door-to-door salesperson. When she goes to a house, the probability that she will make a sale is 0.27. This probability is constant and the probability that Cathy will make a sale at a house is independent of sales at other houses. Calculate the variance in the number of sales Cathy will make in a day if each day she approaches 60 houses. Give your answer to 2 decimal places. Variance in number of sales = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 29, 2016, 18:42 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.01.0030A [2 marks] marks] Let X be a normal random variable with a mean of -1.13 and a standard deviation of 4.64. a) The z-score that corresponds to a particular data point (x) is 1.47. Calculate the data point. Give your answer to 2 decimal places. x= b) The area under the standard normal probability density function from negative infinity to 1.47 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.02.0030A [2 marks] marks] The coffee company American Expresso has a new promotion where "if you don't get your take away coffee within 180 seconds, it's free!". However, far too many coffees seem to have been given away since the promotion began. American Expresso has commissioned an independent study which found that the time to prepare a take away coffee at one of their stores is approximately normally distributed with a mean time of 203 seconds and a standard deviation of 25 seconds. You may find this standard normal table useful throughout the following questions. a) Calculate the percentage of take away coffees that are given to customers for free according to the promotion. Give your answer as a percentage to 1 decimal place. Percentage of free coffees = % b) Shareholders are extremely unhappy with the terms of the promotion and suggest that the time limit should be such that at most only 2.5% of take away coffees are given for free under the promotion. Calculate the time limit such that this requirement is satisfied. Give your answer as a whole number. Time limit = 3 of 3 seconds ID: MST.FET.PD.ND.03.0020A [3 marks] marks] You consider yourself a bit of an expert at playing rock-paper-scissors and estimate that the probability that you win any given game is 0.5. In a tournament that consists of playing 40 games of rock-paper-scissors let X be the random variable that is the of number games won. Assume that the probability of winning a game is independent of the results of previous games. You should use the normal approximation to the binomial to calculate the following probabilities. Give your answers as decimals to 4 decimal places. a) Find the probability that you win at least 24 of the games. P(X 24) = b) Find the probability that you win less than 15 games. P(X < 15) = c) Find the probability that you win between 20 and 30 games. P(20 X 30) = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 29, 2016, 18:42 http://www.perdisco.com.au