Into to Statistics Jeopardy

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Probability Distn

Into to Statistics JeopardyProbability

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Credits

Probability - 100

Answer

Which of the following is not a valid probabilitya.) 2/3b.) 1/8c.) .70d.) 5/4

Probability - 200

Answer

On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

a.) ¼b.) ¾c.) ½d.) 1

Probability - 300

Answer

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected, what is the probability that it is blue?

a.) 1/4 b.) 1/3c.) 1/5d.) 1/9

Probability - 400

Answer

If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years.

a.) 31/365b.) 1/31c.) 1/365d.) 1/12

Probability - 500

Answer

An assignment of probability must obey which of the following?

a) The probability of any event must be a number between 0 and 1, inclusive.

b) The sum of all the probabilities of all outcomes in the sample space must be

exactly 1. c) The probability of an event is the sum of the

outcomes in the sample space which make up the event.

d) All of the above. e) A and B only.

Probability - 600

Answer

A class consists of 61 students, 10 of which are women. If a student is chosen at random, what is the probability that the student is not a women?

a.) 10/61b.) 1/61c.) 51/61d.) 10/51

Probability - 100 Answer

Which of the following is not a valid probability

d.) 5/4

Probabilities are always a value between zero and 1 inclusive. Since 5/4 is greater than 1, it cannot be a valid probability.


On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

a.) ¼

The numerator in our fraction indicates the number of correct choices, the denominator is the total number of choices.


A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected, what is the probability that it is blue?

a.) 1/4

There are 3 blue marbles out of a total of 12 marbles, so the probability of drawing a blue marble is 4/12 which reduces to 1/4


If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years.

a.) 31/365

There are 31 days in May out of 365 possible birthdays. (Note: since not all months have the same number of days, we must use days instead of months to find the probability.)


An assignment of probability must obey which of the following?

a) The probability of any event must be a number between 0 and 1, inclusive.

b) The sum of all the probabilities of all outcomes in the sample space must be

exactly 1. c) The probability of an event is the sum of the

outcomes in the sample space which make up the event.

d) All of the above.

a, b, and c are all true statements


A class consists of 61 students, 10 of which are women. If a student is chosen at random, what is the probability that the student is not a women?

c.) 51/61

If there are 61 students, 10 of which are women, then there must be 51 (61-10) which are not women. So the probability of not selecting a woman is 51/61

Probability Distn - 100Probability Distn - 100

Answer

Determine whether the following is a valid probability distribution

X 1 2 3 4

P(x) 0.037 0.200 0.444 0.296

a.) Yes b.) No


Answer


X 0 1 2 3 4 5

P(x) 0.129 0.312 -0.094 0.084 0.192 0.375

a.) Yes b.) No


Answer

In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distn for the number of adults (among 4 randomly selected adults) who have a college degree

X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the probability that there are at least 2 with college degrees.

a.) 0.3456b.) 0.8208c.) 0.4752d.) 0.5248


Answer

X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the probability that there are less than 3 people who have college degrees.

a.) 0.3456b.) 0.8704c.) 0.5248d.) 0.1296


Answer

X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the expected number (the mean number) of people with college degrees from 4 randomly chosen people.


Answer

X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the standard deviation for the number of people who have college degrees out of 4 randomly selected people

Probability Distn - 100 Ans.Probability Distn - 100 Ans.


X 1 2 3 4

P(x) 0.037 0.200 0.444 0.296

b.) No

0 ≤ P(x) ≤ 1—This condition is met∑ P(x) = 1– The sum of the probabilities = .977 which ≠ 1---so this condition is not met and the distn is not valid


b.) No

0 ≤ P(x) ≤ 1—This condition is not met and the distn is not valid∑ P(x) = 1– The sum of the probabilities = 1

X 0 1 2 3 4 5

P(x) 0.129 0.312 -0.094 0.084 0.192 0.375



X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the probability that there are at least 2 with college degrees.

b.) 0.8208

The probability of at least 2 having college degrees is found by finding the sum of 2, 3, and 4 having degrees


X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

Find the probability that there are less than 3 people who have college degrees.

c.) 0.5248

The probability of less than 3 people having college degrees is found by finding the sum of 2, 1, and 0 having degrees= .0256+.1536+.3456


X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

To find the expected value (the mean) of the distribution

μx = ∑ x •P(x) = 0(.0256) + 1(.1536) + 2(.3456) + 3(.3456) + 4(.1296)=

2.4

TI-Tips:X’s in list 1: P(x) in list 2:1-var stats L1, L2


X 0 1 2 3 4

P(x) 0.0256 0.1536 0.3456 0.3456 0.1296

To find the standard deviation:σ=√∑(x-μ)2•P(x)

(0-2.4)2•.0256 + (1-2.4)2•.1536 + (2-2.4)2•.3456 + (3-2.4)2•.3456 + (4-2.4)2•.1296 = .9798

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Questions have come from the Test Bank for

Basic Practice of StatisticsAnd

Essentials of Statistics

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Into to Statistics Jeopardy