Free Printable Special Discrete Distribution

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Special Discrete Distribution

Total questions: 50

Worksheet time: 4hrs 42mins

Name

Class

Date

Which of the following is NOT an assumption of the Binomial distribution?

All trials must be independent.

Each trial must be classified as a success or a failure.

All trials are dependent on each other.

The number of successes in the trials is counted.

Which of the following is false about binomial probabilities?

Their distributions are approximately symmetric.

Trials must be fixed.

Events musts be independent.

The probability of success must be 0.50

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood?

0.088

0.697

0.214

0.303

4. When rolling two dice, the probability of rolling doubles is ⅙. Suppose that a game player rolls the dice four times, hoping to roll doubles. What is the probability the player gets doubles more than twice in 4 attempts?

0.016

0.00077

0.132

0.004

Bob is taking a 100 question test. They have a 90 % probability of getting any one question correct. WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they will answer EXACTLY 70 questions correctly?

₁₀₀C₇₀ ( 0.18 )³⁰ ( 0.90 )⁷⁰

₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁶⁰

₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

₉₉C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

Find the mean of a binomial distribution with n=50 and p=0.4

Find the variance of a binomial distribution with 50 trials and p= 0.4

Find the standard deviation of a binomial distribution with n=50 and p=0.4 (Round to the nearest tenth)

4.2

3.5

12.0

6.2

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

Yes

No, the trials are not independent.

No, there are more than 2 outcomes

10.

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Do not replace the card. Repeat the process 5 times. Let X = the card you observe.

Yes

No, the trials are not independent.

No, there are more than 2 outcomes

11.

What is the parameter of Poisson distribution?

$\mu$

$\sigma$

$\lambda$

12.

Poisson is a __________ probability distribution

random

discrete

continuous

13.

Poisson distribution expresses the probability of events occurring in a fixed interval of _______ or _______.

time, distance

time, space

distance, space

14.

If the mean of a Poisson distribution is 4,what is its variance?

15.

The mean number of accidents per month at a certain intersection is 3.What is the probability that in any given month exactly 4 accidents will occur at this intersection?

0.081

0.672

0.168

16.

A certain maternity wind has a mean number of 6 babies born a day. what is the probability of 7 babies being bornin this maternity wing on any given day?

0.1377

0.1490

0.8571

17.

If X $\sim$ $P_o$ (1.8), find P(2<X<5)

0.5008

0.2590

0.2330

18.

Paul expected to receive 4 emails in a week.Find the probability of receiving 6 emails for the next 2 weeks?

0.1221

0.1041

0.0531

19.

The random variable, X has the binomial distribution X~B(9,0.25), find P(X=4)

0.1657

0.1168

0.2336

0.3504

20.

The random variable Y has binomial distribution Y~B(10,0.4). Find P(3<Y<6)

0.6665

0.7779

0.4515

0.2508

21.

The random variable T has binomial distribution T~(40,0.5). Find P(T≤12)

0.0032

0.0051

0.9968

0.0083

22.

The probability Ali wins a chess game is 0.4. Given that he plays only 5 games a week, find the probability that in any week he wins at least 2 games.

0.6630

0.3370

0.9222

0.3456

23.

A ball manufacturer claims that only 15% of his balls are defective. If Ali has 6 of these balls to play with at a ball game, find the probability at most 4 balls will be defective.

0.9941

0.0059

0.9996

0.9527

24.

A new surgical procedure is successful 85% of the time. the procedure is performed 8 times and it can be assumed that it is independent each time. Find the expected value of the successful operations.

1.02

6.8

0.1275

1.2

25.

If X~Po(1.8), find P(2≤X≤4)

0.4285

0.7983

0.5008

0.7260

26.

Salmi expected to receive 4 emails in a week. Find the probability of receiving 8 emails for the next 2 weeks.

0.0511

0.0297

0.5470

0.1395

27.

If X~Po(λ) and P(X=0) = 0.0025, find λ.

28.

A rental car service center company has 5 cars available for rental each day. Assume that each car is rented out for the whole day and that the number of cars rented out each day is randomly distributed with a mean of 2. Find the probability that the company cannot meet the demand for cars on any one day.

0.0166

0.0527

0.9473

0.0361

29.

What is the probability that a family doesn't have a baby girl until their third child?

0.13

0.15

0.05

0.88

30.

If the probability that a house in your neighborhood has a dog is 60%, what is the chance that you find a house with a dog before the fifth house?

0.97

0.99

0.02

0.04

31.

Peyton Manning completes 67% of his passes. What is the probability that it takes more than four throws to complete his first pass in a game?

0.99

0.01

0.04

0.96

32.

Find the probability that LeBron James makes a three-point shot on or before his seventh attempt assuming he makes 31.5% of all three-pointers.

0.97

0.03

0.07

0.93

33.

In hockey, 5 players from each team take shots if the game ends in a tie (a shootout). The chances of making a goal in a shootout is low, only 14%. If the Caps and Penguins go into a shootout, what is the probability that the first goal scored is after the first four shots?

0.64

0.47

0.45

0.55

34.

The local Chipotle is running a promotion where each large drink cup has a large pull-off tab that reveals a prize (free burrito!) or the message "Try again next time." Chipotle claims that 25% of the cups have tabs with a prize. You visit Chipotle to try to win. What is the probability that you win on your third visit?

0.86

0.14

0.42

0.58

35.

If you want to know how many trials you will need before your first success, use the ????? model.

Geometric

Binomial

Normal

Calculator

36.

If you want a certain number of successes in a set amount of trials, use the ????? model.

geometric

binomial

normal

calculato

37.

A basketball player has made 80%, of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he makes his first basket on his fourth foul shot

0.00128

0.1024

0.08192

0.0064

38.

A basketball player has made 80%, of his foul shots during the season. How many tries would you expect him to take until he makes a shot?

1.25

4.47

0.56

39.

If Mobius draws 7 cards out of a deck with replacement, what is the probability that he gets the first heart in 6 attempts or fewer?

0.18

0.82

0.06

0.76

40.

A fair die is cast 9 times. What is the probability of obtaining two 6's?

0.167 (3 d.p)

^{0.28 (2 d.p)}

0.83 (2d p)

0.1328

41.

A basketball player has made 80%, of his foul shots during the season.

Assuming the shots are independent, find the probability that in tonight's game he misses for the first time on his fifth foul shot

0.00128

0.0198

0.08192

0.0128

42.

A basketball player has made 80%, of his foul shots during the season.

Assuming the shots are independent, find the probability that in tonight's game he makes his first basket on his fourth foul shot

0.00128

0.1024

0.08192

0.0064

43.

A basketball player has made 80%, of his foul shots during the season.

Assuming the shots are independent, find the probability that in tonight's game he makes his first basket on one of his first 3 foul shots

0.24192

0.16

0.992

0.8

44.

A die is tossed 10 times. What is the probability of getting four sixes ?

0.00077(2 significant figures)

0.054 (2 significant figures)

0.48 (2 significant figures)

0.72 (2 significant figures)

45.

In a game of chess against a particular opponent, the probability that Bakbergen wins is 0.6

He plays 6 games against his opponent. What is the probability that Bakbergen will lose the second game and the 4th game and win the others?

0.020736

0.013824

0.009216

0.006144

46.

In a game of chess against a particular opponent, the probability that Bakbergen wins is 0.6

He plays 6 games against his opponent. What is the probability that Bakbergen will win exactly four games ?

0.043008

0.31104

0.020736

0.13824

47.

In a game of chess against a particular opponent, the probability that Bakbergen wins is 0.6

He plays 6 games against his opponent. What is the probability that Bakbergen will lose at least four games?

0.036864

0.004096

0.1792

0.13824

48.

20% of the items produced by a machine are defective. Four items are chosen at random. Find the probability that none of the chosen items are defective

0.0064

0.625

0.0256

0.4096

49.

Five unbiased coins are tossed.

Find the probability of getting three heads and two tails

0.625

0.3125

0.15

0.125

50.

0.490

0.224

0.180

0.423

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Special Discrete Distribution

Total questions: 50

Worksheet time: 4hrs 42mins

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