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# MTH 157 Week 3 Checkpoint Solution

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Date Created: 11/06/15

Math 157 Week 3 Checkpoint Assignment Due Day 5 Friday Instructions In order to complete your checkpoint in an organized and efficient manner please use this template to type your work and answers Save this template to your computer complete the problems showing all work without using a calculator and post as an attachment to your ltIndividualgt forum If you cannot read the problem on this template refer to the eTextbook on the course aXcess materials page PROBLEM TYPE YOUR SOLUTIONS HERE Section 94 pp 530 532 2 The odds of drawing a spade and a heart are without replacement In Exercises 14 consider the experiment of drawing two cards without replacement from an ordinary deck of 52 playing cards PSpade PSpade 1352 l3 51 169 2652 006372 2 What are the odds in favor of drawing a spade and a heart Section 94 pp 530532 8 We have the following possible outcomes from ipping a coin 3 times 8 What are the odds in favor of getting at least one head in three successive ips of a HHH cor n HHT HTH HTT THH THT TTH TTT So there are 7 out of 8 cases in which we get at least one head The odds are 78 0875 Section 94 pp 530532 36 36 On a TV game show the contestant is EX 1340000 3 50 40053 3 13351 asked to select a door and then is rewarded with the prize behind the door selected If the doors can be selected with equal probability what is the expected value of the selection if the three doors have behind them a 40000 foreign car a 3 silly straw and a 50 mathematics textbook Section 94 pp 530532 38 The expected value of winning is 38 Sam bought 1 of 250 tickets selling for 2 in a game with a grand prize of 400 EX 400250 160 Was 2 a fair price to pay for a ticket to play 39 7 thls game39 No the ticket is overpriced at 2 Section 94 pp 530532 48 EX 16 1 2 3 4 5 6 216 35 48 The game of dots is played by rolling a falr we and recelvmg 1 for each dot A fair price would be 350 for each roll showing on the top face of the die What cost should be set for each roll if the game is to be considered a fair game PROBLEM TYPE YOUR SOLUTIONS HERE Section 95 pp 543544 2 2 In each case consider what you know about the distribution and then explain why you would expect it to be or not to be normally distributed a The wealth of the parents of students attending your school b The values that a group of fourthgrade students would give for the length of a segment that they measured with a ruler c The SAT or ACT examination scores in mathematics for students who were in your high school graduation class d The weights of all incoming freshman students at yourschool a I would expect the wealth of the parents to be normally distributed Most people are middle class but a few have very wellpaid executive or professional jobs and a few have very lowpaid or only part time jobs b The values on the length of the segment would be normally distributed with most of the readings around the actual length of the segment and a few lower and higher estimates due to personal biases in observation c The SAT s in math would definitely be normally distributed with most people scoring around 550 or so around the 50th percentile and the frequency of scores decreasing for lower or higher scores Very few people would obtain an 800 or a 350 d The weight would also be normally distributed with most freshmen being around their healthy weight for their height some people being overweight and some being underweight Section 95 pp 543544 8 8 The number of accidents that occur at the intersection of Pine and Linden streets between 3 pm and 6 pm on Friday afternoons is 0 1 2 or 3 with probabilities of 084 013 002 and 001 respectively A Graph this probability distribution B What is the expected value for the random variable given the number of accidents Probability Distribution Plxl quotI 0 1 2 3 4 Accidents x bEX0084 101320023001013 004003 020 Section 95 pp 543544 12 12 The mean systolic blood pressure of adult males is normally distributed with a mean of 138 millimeters of mercury and a standard deviation of 97 What percent of adult males have blood pressure between 16128 and 1649 Z X u stdev 21 16128 138 97 24 22 1649 13897 277 Using the Zscore table the area between these two values of Z is 09972 09918 00054 which corresponds to a percentage of 054 PROBLEM TYPE YOUR SOLUTIONS HERE Section 95 pp 543544 14 14 A study of motor vehicle rates in the 50 states reveals that traf c death rates deaths per 100 million motor vehicle miles driven can be modeled by the normal curve The data suggest that the distribution has a mean of 53 and a standard deviation of 13 Sketch the normal curve showing the mean and standard deviation Mle lm The mean is at 53 and the standard deviation is 13 Section 95 pp 543544 20 20 Battery Power Problem A certain type of thermal battery for an airplane navigation device backup power has a mean life of 300 hours with a standard deviation of 15 hours What proportion of these batteries can be expected to have lives of 322 hours or less Assume a normal distribution of backup power device lives Z322 300 15 22 15 147 Looking in a Z score table PZlt147 09292 The proportion is 9292 of all batteries can be expected to have lives of 322 hours or less Section 96 pp 554555 2 2 How many 4character license plates are possible with 2 letters from the alphabet followed by 2 digits if repetitions are allowed if repetitions are not allowed Note 2 answers are required We have 26 letters in the English alphabet a If repetitions are allowed 26 26 10 10 67600 b No repetitions allowed 2625 gtllt10gtllt958500 Section 96 pp 554555 4 4 How many batting lineups of the nine players can be made for a baseball team if the catcher bats rst the shortstop second and the pitcher last We have then only 6 positions to play With 6543216720 Section 96 pp 554555 8 8 A class elects two of cers a president and a secretarytreasurer from its 12 members How many different ways can these two of ces be lled from the members of the class The first office can be occupied by 1 out of 12 people and the second by 1 out of the 11 people left 12 11 121 different ways PROBLEM TYPE YOUR SOLUTIONS HERE Section 96 pp 554555 10 10 Five numbers are to be picked without repetition from 44 numbers to determine the winner of the Fortune Five game in the state lottery If the order of the numbers is insigni cant how many different ways can a winning quintuple be selected What is the probability of winning a Different ways of winning quintuple 44 43 42 41 40 130320690 b Chances of winning with a single ticket is 1 130320690 7673 E9 Section 96 pp 554555 26 26 A ship carries exactly 10 different signal ags If each possible combination and ordering of 4 of these ags connotes a speci c message how many signals can be sent with these ags taken 4 at a time This is a problem of permutations How many permutations can we have in a set of 10 elements taking 4 different elements at a time P1041010 4106789105040 Section 96 pp 554555 28 28 A student asks quotWhat s wrong with the argument that the probability of rolling a double 6 in two rolls of a die is because quot Write an explanation of your understanding of the student s misconception What is wrong is that we actually have two rolls of a die ie two different events instead of a single event as implied in the rolling a double 6 Section 96 pp 554555 38 38 Estimate the number of personally constructed greeting cards possible at a machine if there are 12 designs 30 messages 18 closings and 10 different paper stocks on which to print the card Indicate how you made your estimate How valid was your estimate The estimate would be about 10 30 20 10 60000 made by rounding down the 12 to a 10 and rounding up the 18 to a 20 The actual number is 12 30 18 10 64800 The estimate is 8 smaller than the actual number ie it s a pretty good estimate Chapter 9 Review 2 2 Ajar contains four marbles each a different color red blue green and yellow If you draw two marbles from the jar one after another replacing the rst before drawing the second what is the probability of getting a two red marbles b a red marble on the rst draw and a green marble on the second draw c at least one red marble and one green marble d no yellow marbles We have replacement and there are a total of 4 marbles each with a different color a P2 red 025 025 00625 b Pred first green next 025 025 00625 c Since we have only two draws this is equivalent to the sum of Pfirst is red second is green Pfirst is green and second is red 025 025 025 025 0125 d Pno yellow marbles 1 Pboth yellow marbles 1 025025 1 00625 09375 PROBLEM TYPE YOUR SOLUTIONS HERE Chapter 9 Review 12 We have the possible combinations 12 Suppose that pizzas can be ordered in four sizes small medium large and ini Sizes gtxlt crusts gtxlt Meats gtllt Cheeses 4 gtllt 3 gtllt 4 gtllt 2 12 gtllt 8 size with three crust choices thin thick and Chicago style four choices of meat sausage pepperoni hamburger and none and two types of cheese regular or double 108 different styles of pizzas How many different styles of pizza can be ordered

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