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

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

~ FE Review-Probability & Statistics Tomass 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


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FE Review-Probability & Statistics 1 Tomas·s fev0<1te colors are blue and l(re~u. He has I bltlt' shirl. I gr...-n shirt. 1 hlu,· littt. 1 gr...-n starf. I blue pair of

pa111,_ end

1 grfi'n p11ir of

pi111ts Tomas selects one or these garments at random Let A be the event that he selects a blue garment and let B be the event that he chooses a shirt Which of the following statements are true? Select al that apply

~

P( A I B) P( A). the probab1l1ty that Tomes selects a blue garment given that he hes chosen a

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. The outcome or events A and B are dependent on each other

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

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FE Review-Probability & Statistics 2

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

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FE Review-Probability & Statistics 3

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%

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FE Review-Probability & Statistics 4

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
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FE Review-Probability & Statistics 5

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
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FE Review-Probability & Statistics 6

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

  • f 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
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FE Review-Probability & Statistics 7

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%

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FE Review-Probability & Statistics 8

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%
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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

  • hms. 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

FE Review-Probability & Statistics 9

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FE Review-Probability & Statistics 10

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

  • f 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
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FE Review-Probability & Statistics 11

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

  • btained. 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
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FE Review-Probability & Statistics 12

A ag co~tains 4 , green sades 2 bl . e socks a d 5 i red socks. l' o socks are

iremoved.

a is t · e p o abT · at t e first sock is,

red a d

e seeo d

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FE Review-Probability & Statistics 13

Five people gather for

a

dinner party. The

probability that no two

  • f

them haw the same birthday is:

  • A. 0.93

I!. 0.9$

  • C. 0.97

0 . 0.99

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FE Review-Probability & Statistics 14

The annual rainfall in a city can be approximated as a Gaussian

  • distribution. The mean rainfaD

is 15

inches and the standard deviation is 2 inches.

The probability that the

rainfall in any year is greater than 18 inches Is: A. 7-/o

  • B. 9%
  • C. 11%
  • D. 13o/o

The probability that the rainfall in any year is between

18 and 20 inches is:

  • A. 6%
  • 8. 8%
  • c. 10%
  • D. 1

2%

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FE Review-Probability & Statistics 15

A rare dise•se afflicts 1 in 1000 adwts. tf

a pe1$on has lhe disease, a test wlll show positive 99% of the time. If a peroon does

net have the disease. the re3tJt will show

positive 2% of

the time. For• randomly

tested person that tests posttive, the probability thal the individual has the disease is:

  • A. 0.001
  • B. 0.034
  • C. 0.()4

7

  • D. 0.990
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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
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Tho avorago wcrght that most pcoplo stort a populor ~ dieting program 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

dovlallon of 20 p0unds Al tho 2.5°

/4 tovol of

  • slgnmcanco. can you dctcrmlno ,f tho and1

11Lduills of

lhls populor woighl lo · program havo docro«isod In

weight?

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