P( A I B) A). the probab1l1ty that Tomes selects a blue garment - PDF document

~ FE Review-Probability & Statistics Tomas·s fev0<1te colors are blue and l( re~u. He has I bltlt' shirl. I gr...-n shir t. 1 hlu,· littt . 1 gr...-n starf. I blue pair of pa111,_ end 1 grfi'n p11ir of pi111 ts these garments at random Let A be the event that he selects a blue garment Tomas selects one or and let B be the event that he chooses a shirt Wh i ch of the fol l owing sta t ements are true? Select al that apply P( A I B) A). the probab1l1ty that Tomes selects a blue garment given that he hes chosen a P( shirt is equal to the probability that Tomas selects a blue garmenL P(B I A) - P(B). the probab11,ty that Tomas selects a Shirt given that he has chosen a blue garment 1s equal to the probabthty that Tomas selects a Shn1. Events A and B are independent events. events A and B are dependent on each other The outcome or P(A and B) P(A) · P(B) . the probl!b1lity that Tomas selects a blue garment that ,s a shirt is equal to the probabthty that Tomas selects a blue garment mulbpl1ed by the probab1lrty that he selects a shirt 1

FE Review-Probability & Statistics Probability & Sample Space How many different 5 card hands can be dealt from a deck of 52 cards? a) 52!/47! b) 2,598,960 c) 52!/5! d) 12,994,800 Compound Probability A lottery draw consists of picking balls numbered 1 through 60 from a rotating drum. What is the probability of drawing the #20 ball or an odd numbered ball during the first draw? a) 29/60 b) 1/60 c) 30/60 d) 31/60 2

FE Review-Probability & Statistics Conditional Probability Given the EIT exam has an 50% pass rate, and 5% of the people who take the exam have previously failed. What is the probability of passing the exam on the first go around, if the probability of passing the exam for those who have previously failed is 80%. a) about 48% b) about 50% c) about 60% d) about 54% 3

FE Review-Probability & Statistics Independent Events If a baseball player has a probability of 0.25 for hitting a pitched ball, what is the approximate probability that the player will miss three pitches in a row? (Probability of missing the first pitch, second pitch, and the third pitch) a) 0.58 b) 0.42 c) 0.25 d) 0.75 Discrete Distributions • Consider the following discrete probability distribution • X 2 3 4 5 6 7 8 9 10 11 12 P[X] 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 Which one of the following statements is incorrect? • a) Sum of all P{X} = 1 • b) P{2} = 1/36 • c) P{7} + P{11} = 8/36 • d) P{5.5} = 1/4 4

FE Review-Probability & Statistics Mean, Mode, Median • A medical study focusing on when people first develop heart problems has recorded the following data: Age 0-10 10-20 20-30 30-40 40-50 50-60 70+ People 18 140 267 960 1200 1720 800 According to this study by what age do at least 50% of the people begin to experience heart problems • a) by the age of 65 • b) by the age of 40 • c) by the age of 60 • d) by the age of 50 Sample Mean The following data was recorded from a laboratory experiment. Number 1 2 3 4 5 6 Data 22 25 24 25 21 27 What is the sample mean of the recorded data? • a) 3.5 • b) 6.0 • c) 4.0 • d) 4.8 5

FE Review-Probability & Statistics Sum of RV Four resistors from a batch of 100-watt resistors are connected in series. The resistors have mean resistance of 100 ohms with a standard deviation of 1 ohm. What will be the standard deviation of the series resistance of the four resistors? • a) 100 ohms • b) 4 ohms • c) 2 ohms • d) 16 ohms 6

FE Review-Probability & Statistics Binomial Distribution An auto dealer orders 50 new automobiles for resale. If 1% of the automobiles produced are shipped defective, what is the approximate probability that the auto dealer will receive at least one defective automobile? a) 50% b) 35% c) 30% d) 25% 7

FE Review-Probability & Statistics Normal Distribution The results if the EIT exam had indicated a mean score of 68 and standard deviation of 14. Assuming a normal distribution, what percent of the people scored above 95 ? • a) around 7.5% • b) about 5% • c) a little more than 2.5% • d) a little less than 2.5% 8

FE Review-Probability & Statistics Normal Distribution A printed circuit board manufacturer produces 1000 boards per day having a mean impedance value of 100 ohms. QA tests indicate 80% of the boards produced have an impedance between 95 and 105 ohms. If the minimum acceptable impedance range is from 90 ohms to 110 ohms, how many boards are rejected per day? Assume a normal distribution of impedances. • a) 1 • b) 10 • c) 100 • d) 11 9

FE Review-Probability & Statistics Confidence Interval Four resistors from a batch of 100-watt resistors are connected in series. The resistors have mean resistance of 100 ohms with a standard deviation of 1 ohm. What is the 95% confidence limit for the total series resistance of the four resistors? • a) 396.1 to 403.9 • b) 398.2 to 402.8 • c) 402.2 to 404.8 • d) 396.0 to 404.0 10

FE Review-Probability & Statistics Conf Interval of Mean During a routine physical exam of 100 of the 1500 employees at a hospital a mean weight of 175 lbs and sample standard deviation of 15 lbs was obtained. At a 95% confidence level, what would be the interval (range) of the mean weight of all the employees? • a) 172 to 178 • b) 170 to 180 • c) 173 to 179 • d) 171 to 179 11

FE Review-Probability & Statistics A ag co~ ta ins 4 , green sades 2 bl . e socks a d 5 i red socks. l' o socks are a is t · at t e ir emoved. e p o abT · first sock is, red a d e seeo d 12

FE Review-Probability & Statistics a Five people gather for dinner party. The probability that no two of them haw the same birthday is: A. 0.93 I! . 0.9$ C. 0.97 0 . 0. 99 13

FE Review-Probability & Statistics The annual rainfall in a city can be The probability that the approximated as a Gaussian rainfall in any year is between distribution. The mean rainfaD is 18 and 20 in ches is: 15 inches and the standard A. 6% deviation is 2 inches. 8. 8% c. 1 0% D. 1 2% The probability that the ra infall in any year is greater than 18 i nches Is: A. 7-/o B. 9% C. 11% D. 13o/o • 14

FE Review-Probability & Statistics A rar e d ise •se afflicts 1 in 1000 adwts. tf a pe1$on h as lhe di sease , a test wlll show positive 99 % of the time. If a peroon doe s net have the disease . the re3 tJt will show positive 2% of the tim e. For• randomly tested person that tes ts posttive, the prob ab ility th al the i nd ivid ua l h as the disease is : A. 0. 001 B. 0.034 C. 0. ()4 7 D. 0.990 15

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The final scores on a test are normally distributed with a mean of 72 and a standard deviation of 10 . What is most nearly the probability that a student's score will be between 65 and 78? A. 0.4196 B. 0.4837 C. 0. 5161 D. 0.6455 23

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FE Review-Probability & Statistics Tho avorago wcrght that most pcoplo stort a populor ~ dieting prog ra m Is 300 pounds Aftor 4 wooks ,n tho progrnrn. you loko o somplo of 28 individuals and Ond Ulo moan lo bo 290 pounds w11h ta ~tandord d ov la llon of 20 p0unds Al th o 2. 5° /4 tovo l of slgnmcanco. can you dctcrmlno ,f th o and 1 11Lduills of lh ls populor woighl lo · program havo docro«isod In weight? 25

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