Sophia Milestone 3 exam

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School

Capella University *

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2001

Subject

Statistics

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Jan 9, 2024

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docx

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Uploaded by AdmiralMusic12572

26/27 that's 96% RETAKE 26 questions were answered correctly . 1 question was answered incorrectly . 1 Using the Venn Diagram below, what is the conditional probability of event A occurring, assuming that event B has already occurred [P(A| B)]?  0.05  0.22  0.10  0.71 RATIONALE To get the probability of A given B has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.1. The probability of B is all of Circle B, or 0.1 + 0.35 = 0.45. CONCEPT Conditional Probability Report an issue with this question 2 Mark noticed that the probability that a certain player hits a home run in a single game is 0.175. Mark is interested in the variability of the number of home runs if this player plays 200 games.

If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games? Answer choices are rounded to the hundredths place.  28.88  5.37  5.92  0.14 RATIONALE In this situation, we know: n = sample size = 200 p = success probability = 0.175 We can also say that q, or the complement of p, equals: q = 1 - p = 1 - 0.175 = 0.825 The standard deviation is equivalent to the square root of the variance. First, find the variance. The variance is equivalent to n*p*q: Now, take the square root to find the standard deviation: CONCEPT Normal Distribution Approximation of the Binomial Distribution Report an issue with this question 3 What is the probability of NOT rolling a four when rolling a six sided die? 

   RATIONALE Recall that the probability of a complement, or the probability of something NOT happening, can be calculated by finding the probability of that event happening, and then subtracting from 1. Note that the probability of rolling a four would be 1/6. So the probability of NOT rolling a four is equivalent to: CONCEPT Complement of an Event Report an issue with this question 4 Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results. Boys Gi Apple 66 4 Orange 52 4 Mango 40 5 If you were to choose a boy from the group, what is the probability that mangoes are his favorite fruit? Answer choices are rounded to the hundredths place.  0.39  0.13

 0.75  0.25 RATIONALE The probability of a person picking mangoes as his favorite fruit given he is a boy is a conditional probability. We can use the following formula: Remember, to find the total number of boys, we need to add all values in this column: 66 + 52 + 40 = 158. CONCEPT Conditional Probability and Contingency Tables Report an issue with this question 5 Kate was trying to decide which type of frozen pizza to restock based on popularity: pepperoni pizza or sausage pizza. After studying the data, she noticed that pepperoni flavors sold best on the weekdays and on the weekends, but not best overall. Which paradox has Kate encountered?  Benford's Law  Simpson's Paradox  False Negative  False Positive RATIONALE This is an example of Simpson's paradox, which is when the trend overall is not the same that is examined in smaller groups. Since the sale of pepperoni flavors on weekend/weekdays is larger but this trend changes when looking at overall sales, this is a reversal of the trend.

CONCEPT Paradoxes Report an issue with this question 6 Ryan is playing a multiplication game with a pile of 26 cards, each with a number on them. Each turn, he flips over two of the cards, and has to multiply the numbers. How many possible outcomes are there on Ryan's first turn flipping two cards?  650  676  26  52 RATIONALE We can use the general counting principle and note that for each step, we simply multiply all the possibilities at each step to get the total number of outcomes. If we assume that the numbers are 1 - 26, then the overall number of outcomes is: Note that once a number is chosen it cannot be chosen again. So the number of possible outcomes for the first card would be 26 since they could choose any card number 1 through 26. However, the second card chosen would only have 25 possible outcomes since the first card has already been drawn. CONCEPT Fundamental Counting Principle Report an issue with this question 7

Annika was having fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit). There are 15 cards left in the deck, and five are diamonds. What is the probability that the two cards dealt to Annika (without replacement) will both be diamonds? Answer choices are in percentage format, rounded to the nearest whole number.  10%  13%  33%  29% RATIONALE If there are 15 cards left in the deck with 5 diamonds, the probability of being dealt 2 diamonds if they are dealt without replacement means that we have dependent events because the outcome of the first card will affect the probability of the second card. We can use the following formula: The probability that the first card is a diamond would be 5 out of 15, or . The probability that the second card is a diamond, given that the first card was also a diamond, would be because we now have only 14 cards remaining and only 4 of those cards are diamond (since the first card was a diamond). So we can use these probabilities to find the probability that the two cards will both be diamonds: CONCEPT "And" Probability for Dependent Events Report an issue with this question

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