Probability and Statistics Quiz: Conditional & Binomial Distributions

Question 1 (Mandatory) 8 / 8 points Assume the following joint and marginal probabilities: P(Yes | Republican) is a ________ probability. Question options: Joint Marginal Conditional Hide question 1 feedback Conditional probability = joint probability divided by a marginal probability corresponding to the condition. Question 2 (Mandatory) 8 / 8 points Given the following partial relative frequency table Republican Democrat Independent Male 0.158 0.182 0.102 Female 0.103 0.133 ? Compute P(Female | Democrat) and enter your answer with 3 decimal places. Answer: 0.422 Hide question 2 feedback P(Female | Democrat) = P(Female and Democrat) ÷ P(Democrat) Question 3 (Mandatory) 8 / 8 points Given the following partial relative frequency table Republican Democrat Independent Male 0.116 0.196 0.139 Female 0.122 0.101 ? Compute P(Republican | Male) and enter your answer with 3 decimal places. Answer:

0.257 Hide question 3 feedback P(Republican | Male) = P(Republican and Male) ÷ P(Male) Question 4 (Mandatory) 12 / 12 points Assume breast cancer affects 0.004 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 have it). Assume mammograms are  0.90 accurate detecting people who actually have breast cancer (true positive rate)  0.90 accurate for people who do not have breast cancer (true negative rate). Compute the probability that a female who tests positive for breast cancer has breast cancer and enter your answer with 3 decimal places. Answer: 0.035 Hide question 4 feedback EXAMPLE Question 5 (Mandatory) 8 / 8 points Choose all of the correct answers for the characteristics of a Binomial Probability Distribution. Question options: An example of a binomial trial is rolling a die. An example of a binomial trial is flipping coins.

Each binomial trial has only 2 possibilities. The variables are continuous. The binomial trials are dependent on each other. The variables are discrete. There can be three or more outcomes of each binomial trial. The binomial trials are independent of each other. Hide question 5 feedback bi + nomial means two names (events), like heads or tails in a toss of a coin. The binomial random variable is a count of the events of interest in a sequence of trials. So, it is discrete. Question 6 (Mandatory) 8 / 8 points Select all correct answers for the Poisson probability distribution. Question options: The Poisson distribution describes a situation where the probability of success does not remain the same from trial to trial. An example of a Poisson trial is selecting the members of a committee from one business. The variable in a Poisson trial is counted. The Poisson distribution's mean=median=mode. 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 counting the number of misspelled words in a magazine article. The variables in a Poisson trial are measured. Question 7 (Mandato ry) 8 / 8 points Misa earned a score of 80 on her latest exam. The professor determined that all of the scores from this exam had a normal distribution with a mean of 85 and a standard deviation of 5. What is Misa's Z score on her exam?

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Round to three decimal digits. Answer: -1.000 Hide question 7 feedback Z = (Value - Mean) / standard deviation Question 8 (Mandatory) 8 / 8 points Blue Crab lengths have a normal distribution with a mean of 10 inches and a standard deviation of 2 inches. What is the Z value of 10 inches? Round to three decimal digits. Answer: 0 Hide question 8 feedback Z = (Value - Mean) / Standard deviation Question 9 (Mandatory) 8 / 8 points In every normal distribution Question options: The mean = 0 and the standard deviation = 1 The mean is larger than the standard deviation The interquartile range covers 68% of the values The mean and the median are equal. Hide question 9 feedback The normal distribution is symmetric (bell-shaped). Skew = 0. So, mean = median. Question 10 (Mandatory) 8 / 8 points The Standard Normal Distribution is a Normal Distribution with the following characteristics: 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 on ndatory) In a normal distribution, what is the probability of all values larger than 1 standard deviation above the mean as shown: Due to rounding, your result may vary from the answer selections depending on whether you use the online calculator, Excel functions, or Empirical Rule (68 95 99). Choose the closest answer to your result. Question options: 32% 16% 68% There is not enough information to answer the question None of the answers match my calculation. Hide question 11 feedback 68.26% lies within 1 standard deviation of the mean So 100% - 68.26% = 31.74% lies outside 1 standard deviation from the mean This is split equally in the left and right tails. So, half of 31.74%, or 31.75%/2 = 15.87% is in the right tail. This rounds to 16%. Question 12 (Mandatory) 8 / 8 points In a normal distribution, what is the probability of a value between 2 and 3 standard deviations below the mean as shown: Due to rounding, your result may vary from the answer selections depending on whether you use the online calculator, Excel functions, or Empirical Rule (68 95 99). Choose the closest answer to your result. Question options:

2.35% .15% None of the answers match my calculation. -.15% -2.35% Hide question 12 feedback P(Z ≤ 2) - P(Z ≤ 3), by Empirical Rule 1/2 x (99.72% - 95.44%) = 2.35%

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Week 4 Quiz

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