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##### Midterm exam part 2

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**Question**

Question;Midterm Exam (Part 2);There are six (6) total questions over two (2) pages.;Part 2 is worth sixty (60) total points.;Please ensure that you have also completed the;multiple choice portion (Part 1) of this exam.;Name;Answer the following six (6) questions.;Show all work. Partial credit may be awarded.;1.;The finishing process on new;furniture leaves slight blemishes. The;table below displays a manager's probability assessment of the number of;blemishes on one piece of new furniture.;(10 points.);Number of Blemishes;0;1;2;3;4;5;Probability;0.34;0.25;0.19;0.11;0.07;0.04;A);On average, how many blemishes;do we expect on one piece of new furniture?;B);What is the standard deviation;of blemishes on one piece of new furniture?;2.;The probability that a person;catches a cold during the cold-and-flu season is 0.4. Assume that 10 people are chosen at random. (10 points.);A);On average, how many of these;ten people would you expect to catch a cold?;B);What is the standard deviation;of the number of people who catch a cold?;3.;The;number of nails in a five-pound;box is normally distributed with a mean of 563.3 and a standard deviation of;33.2. (10 points.);A);What is the probability that;there are less than 500 nails in a randomly-selected five-pound box of nails?;B);The probability is 0.99 that a;randomly-selected five-pound box of nails contains at least how many nails approximately?;4.;You are the owner of a small;casino in Las Vegas and you would like to reward the high-rollers who come to your casino.;In particular, you want to give free accommodations to no more than 10%;of your patrons. Suppose that the amount;wagered by patrons follows a normal distribution. The mean amount wagered by all patrons is;$287 with a standard deviation of $15.;You should give free accommodations to those individuals who wager over;how much money?;(5 points.);5.;Candidates for employment at a;city fire department are required to take a written aptitude test. Scores on this test are normally distributed;with a mean of 260 and a standard deviation of 51.;A random sample of nine (9) test scores is taken. (10 points.);A);What are the mean and;standard error of the sample mean scores?;B);What is the probability that;the sample mean score is less than 250?;6.;It has been found that 62.1% of;all unsolicited third-class mail delivered to households goes unread. Over the course of a month, a household;receives 100 pieces of unsolicited mail.;(15 points.);A);What is the mean of the sample;proportion of pieces of unread mail?;B);What is the standard error of;the sample proportion?;C);What is the probability that;the sample proportion is greater than 0.60?

Paper#62270 | Written in 18-Jul-2015

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