Stat Asst 2

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8 / 8 points When the probability of event B is affected by the occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability.

Type | by holding down Shift and type \ For independent events A and B, P(B | A) = P(B), and P(A |

B) = P(A) For dependent events A and B

o P(B | A) ≠ P(B). The occurrence of A has changed the probability of B.

o P(A | B) ≠ P(A). The occurrence of B has changed the probability of A.

For dependent events, P(A and B) = P(A) x P(B | A) = P(B) x P(A | B). This is the General Multiplication Rule.

Assume the following joint and marginal probabilities:

When we know the condition that some event has occurred, the table reduces to a row or column matching the condition. For example, when we know that the party is Democrat, the table reduces to the Democrat column:

P(Yes | Democrat) is the probability of event Yes given the condition that the event Democrat has occurred. In condition Democrat, Yes occurs at a rate of 0.15 in 0.40. So P(Yes | Democrat) = 0.15/0.40 = 0.375.

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Supplemental

Course Content Session 3 Lecture beginning p. 13 Additional Reading Video

P(Male | Republican) is a ________ probability.

Question options:

Conditional

Given the following partial relative frequency table

Republica n

Democra t

Independen t

Male 0.144 0.184 0.129 Femal e

0.108 0.185 ?

Compute P(Female | Democrat), and enter your answer with 3 decimal places.

Answer:

0.501

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P(Female | Democrat) = P(Female and Democrat) ÷ P(Democrat)

8 / 8 points Given the following partial relative frequency table

Republica Democra Independen

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n t t Male 0.145 0.161 0.169 Femal e

0.121 0.100 ?

Compute P(Republican | Male), and enter your answer with 3 decimal places.

Answer:

0.305

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P(Republican | Male) = P(Republican and Male) ÷ P(Male)

12 / 12 points Assume breast cancer affects 0.001 of the female population between 45 and 55 years of age.

There are two kinds of positive test results:

True positive (the test indicates you have a disease, and you actually have it)

False positive (the test indicates you have a disease, but you actually do not).

Assume mammograms are

0.90 accurate detecting people who actually have breast cancer (true positive rate)

0.91 accurate for people who do not have breast cancer (true negative rate).

Compute the probability that a female between the ages of 45 and 55 who tests positive for breast cancer has breast cancer, and enter your answer with 3 decimal places.

Answer:

0.009

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https://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

Probability = desired event / all possibilities

In this case the desired event is a true positive test.

All possibilities = true positive test + false positive test

Probability of a true cancer positive test = probability of having cancer * the probability that the test found the cancer.

The false positive = (1 - probability of having cancer) * the probability that the test found cancer (1 - true negative rate.)

P(Cancer)=0.001

P(No cancer)= 1-P(cancer)

=1-0.001

=0.999

P(Test Positive |no cancer)= 1-P(Negative | no cancer)

= 1-0.91

=0.09

[0.001*.90] / [(0.001*0.90) + (0.999*0.09)]

0.0009 / (0.0009) + (0.08991)

0.0009 / 0.9891

= 0.009

8 / 8 points Misa earned a score of 95 on her latest exam. The professor determined that all of the scores from this exam had a normal distribution with a mean of 87 and a standard deviation of 3.

What is Misa's Z score on her exam?

Round to three decimal digits.

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Answer:

2.667

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Z = (Value - Mean) / standard deviation

8 / 8 points Blue Crab lengths have a normal distribution with a mean of 5 inches and a standard deviation of 2 inches.

What is the Z value of 5 inches?

Round to three decimal digits.

Answer:

0

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Z = (Value - Mean) / Standard deviation

8 / 8 points In every normal distribution

Question options:

The mean is larger than the standard deviation

The mean and the median are equal

The interquartile range covers 68% of the values

The mean = 0 and the standard deviation = 1

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In a normal distribution the probability of a value larger than one standard deviation above the mean is:

Question options:

There is not enough information to answer the question

In a normal distribution the probability of a value between 2 and 3 standard deviations below the mean is:

Question options:

.15%

-2.35%

-.15%

2.35%

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8 / 8 points The Standard Normal Distribution is a Normal Distribution with the following characteristics:

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Question options:

The mean is 1 and the standard deviation is 0

The mean is 0 and the standard deviation is 1

The mean and the standard deviation are 0

The mean and the standard deviation are 1

Choose all of the correct answers for the characteristics of a Binomial Probability Distribution.

Question options:

The variables are discrete.

An example of a binomial trial is rolling a die.

There can be three or more outcomes of each binomial trial.

Each binomial trial has only 2 possibilities.

The binomial trials are independent of each other.

An example of a binomial trial is flipping coins.

The variables are continuous.

The binomial trials are dependent on each other.

Select all correct answers for the Poisson probability distribution.

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Question options:

The Poisson distribution's mean=median=mode.

The Poisson distribution describes a situation where the probability of success does not remain the same from trial to trial.

The Poisson distribution describes the number of events occurring in a unit of space or time.

The Poisson distribution is always positively skewed.

An example of a Poisson trial is selecting the members of a committee from one business.

An example of a Poisson trial is counting the number of misspelled words in a magazine article.

The variables in a Poisson trial are counted.

The variables in a Poisson trial are measured.

100 / 100 - 100 %

100 / 100 - 100

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