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# # 6 - Due Wednesday 11:59 PM EDT Description Current Score...

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Due: Wednesday, October 17, 2007 11:59 PM EDT Current Score: 30 out of 30 Question Score Submission Options Description Homework 6 covers random variables, probability distributions, expected value, and standard deviation. Instructions Homework 6 You are allowed four submissions. Due date is 11:59 pm Monday October 15. 1. 2.5/2.5 points Last Response | Show Details All Responses Notes You are planning to take to a trip to Montreal, Canada during the month of April and you want to bring clothing that is appropriate for the weather. The daily high temperature X in degrees Celsius in Montreal during April has an average (expected value) of 10 o C with a standard deviation of 4 o C. You want to convert these Celsius temperatures to o F (degrees Fahrenheit). The conversion of X into degrees Fahrenheit is Y = (9/5)X + 32. a. What is the expected daily high in Montreal during April in degrees Fahrenheit?50 50 b. What is the standard deviation of the daily high temperature in Montreal during April in degrees Fahrenheit?7.2 7.2 2. 4.5/4.5 points Last Response | Show Details All Responses Notes

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In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius: Temperature X 540 o 545 o 550 o 555 o 560 o Probability 0.1 0.25 0.3 0.25 0.1 a. Find the expected value of the temperature X.550 550 b. Find the standard deviation of the temperature X.5.701 5.701 (Use 3 decimal places.) The target temperature is 550 o C. c. What is the expected value of the number of degrees off target, X-550?0 0 d. What is the standard deviation of the number of degrees off target, X-550? 5.701 5.701 3. 7/7 points Last Response | Show Details All Responses Notes "Digital Analysis" is an important new tool auditors use when looking for fraud. Faked numbers in payment records, invoices, expense account claims, and many other settings often display patterns that are NOT present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a surprising fact that the first digit X of numbers in legitimate records are NOT equally distributed between 1 and 9, but follow a distribution known as Benford's Law . The distribution of the first digit according to Benford's Law is shown in the first table below. Benford's Law First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046 If first digits in a set of records appeared "at random," the nine possible digits 1 to 9 all have the same probability, that is, each of the digits 1, 2, . . . , 9 is equally likely to be the first digit. The probability distribution of the first digit Y according to the random model is shown in the table below.

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