MATH 225N Week 4 Quiz Collection (Multiple Versions), Exams of Nursing

Download MATH 225N Week 4 Quiz Collection (Multiple Versions) and more Exams Nursing in PDF only on Docsity! 1 That is correct! Question 1 Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level. We expect that 416 of every 500 coin tosses will result in heads. At the 0.01 level of significance, the coin is likely not a fair coin. There is certainty that the coin is not a fair coin. The results are not statistically significant at the 0.05 level of significance. Answer Explanation Correct answer: At the 0.01 level of significance, the coin is likely not a fair coin. The results of the experiment are significant at the 0.01 level of significance. This means the probability that the outcome was the result of chance is 0.01 or less. Because of this, we can be fairly confident, but not certain, that the coin is not a fair coin. FEEDBACK • • • • Content attribution- Opens a dialog 2 Question 2 Suppose X∼N(11,0.5), and x=12. Find and interpret the z-score of the standardized normal random variable. 5 That is correct! 6 The outlier is 98. The mode is affected by the outlier. The outlier is 98. The mean is affected by the outlier. The outlier is 200. The median is affected by the outlier. The outlier is 200. The mean is affected by the outlier. Answer Explanation Correct answer: The outlier is 200. The mean is affected by the outlier. The data value 200 is significantly different from other data values in the dataset, so 200 is the outlier. The mean is affected by outliers. A data value that is far greater than the rest of the data values will cause the mean to be much greater than it would be if the data value were closer to the rest. In this case, the mean of 104.25 would not be a good measure of the center of the dataset since 7 of the 8 data values are less than 104.25. FEEDBACK • • • • Content attribution- Opens a dialog Question 5 The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: 6, 3, 14, 11, 14, 6 7 That's not right. • Round the final answer to one decimal place. 10 $$std=1.4 • Round the final answer to one decimal place. Answer Explanation CORRECT ANSWERS: Notice that this dataset reflects ages for the entire population of the grandchildren in the family, and this indicates that the calculation should be based on population mean. To calculate the population standard deviation, take the square root of the population variance. Since we are given the variance is 9.7, the standard deviation is 9.7−− −√\approx3.1$_. FEEDBACK • • • • Content attribution- Opens a dialog Question 7 Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 • $\text{std=}3.1$std=3.1 That's not right. That is correct! 11 $$median=26 thousands of dollars Answer Explanation CORRECT ANSWERS: • $\text{median=}26\text{ thousands of dollars}$median=26 thousands of dollars 12 $$mode=3 cards That is correct! It helps to put the numbers in order. 14,19,20,26,33,42,46 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 26. So the median price (in thousands of dollars) of randomly selected trucks at a car dealership is 26. FEEDBACK • • • • Content attribution- Opens a dialog Question 8 Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears. 3,12,3,11,5,5,3,10,12 Answer Explanation CORRECT ANSWERS: If we count the number of times each value appears in the list, we get the following frequency table: Value Frequency • $\text{mode=}3\text{ cards}$mode=3 cards 15 Answer Explanation Correct answer: 16 Min Q1 Median Q3 Max 2 3 5 1 14 1 We can immediately see that the minimum value is 2 and the maximum value is 14. There are 15 values in the list, so the median value is the one where there are 7 values below it and 7 values above it. We see that this happens at the value 5, so that is the median. Now, looking at the lower half of the data, there are 7 values there, and so the median value of that half of the data is 3. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 11. So the five-number summary is Min Q1 Median Q3 Max 2 3 5 1 14 1 FEEDBACK • • • • Content attribution- Opens a dialog Question 10 The box-and-whisker plot shows the number of books read by history students during the last school year. 17 A box and whisker plot with minimum 4, first quartile 6, median 8, third quartile 10, and maximum 15 20 • 43 • • 44 • • 48 • • 64 • • 70 • 21 Answer Explanation Correct answer: 43 44 22 $$mean=16 boxes That is correct! 48 Remember that outliers are numbers that are less than 1.5⋅IQR below the first quartile or more than 1.5⋅IQR above the third quartile, where IQR stands for the interquartile range. The interquartile range is the third quartile minus the first quartile. So we find IQR=79−69=10 So a value is an outlier if it is less than Q1−1.5⋅IQR=69−(1.5)(10)=54 or greater than Q3+1.5⋅IQR=79+(1.5)(10)=94 So we see that 43, 44, and 48 are outliers. FEEDBACK • • • • Content attribution- Opens a dialog Question 12 Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16,14,14,21,15 Find the mean boxes sold. 25 • • 26 $$10 That is correct! • Content attribution- Opens a dialog Question 14 Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains. StudentsgotothebeachdonotgotothebeachTotalgotothemount ains48donotgotothemountains21Total3695 Answer Explanation CORRECT ANSWERS: By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the row of totals in the table, we know that the unknown number plus 48 is 95, so the missing number must be 47. Continuing in this way, we can fill in the entire table: StudentsgotothebeachdonotgotothebeachTotalgotothemount ains103848donotgotothemountains262147Total365995 From this, we can see that the number of students who both go to the beach and go to the mountains is 10. FEEDBACK • • • • Content attribution- Opens a dialog • $10$10 27 Question 15 Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? 30 C D Answer Explanation Correct answer: C Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A box and whisker plot with short whiskers and a short box has values that are less spread out, and hence has a smaller standard deviation. FEEDBACK • • • • Content attribution- Opens a dialog Question 16 Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked them whether or not they had a fear of flying and whether or not they had a fear of heights. The data are shown in the contingency table below. What is the relative risk of being afraid of heights for those who are afraid of flying? Round your answer to two decimal places. Afraid of flyingNot afraid of flyingTotalAfraid of heights7682158Not afraid of heights33370403Total109452561 31 $$10.42 That's not right. 32 $$312 That is correct! Answer Explanation CORRECT ANSWERS: The probability that someone with a fear of flying is afraid of heights is 76109. The probability that someone who does not have a fear of flying is afraid of heights is 82452=41226. The relative risk is then 7610941226≈3.84. This means that in this survey, people with a fear of flying were 384% as likely to have a fear of heights as people without a fear of flying. FEEDBACK • • • • Content attribution- Opens a dialog Question 17 Diana is packing a lunch that will include an orange. Diana has 3 navel oranges, 5 mandarin oranges, and 4 Valencia oranges. If Diana selects an orange at random, what is the probability that she selects a navel orange? • Give your answer as a fraction. Answer Explanation CORRECT ANSWERS: • $3.84$3.84 • $\frac{3}{12}$312 35 100,90,95,89,92,85,95. 36 $$92.3 That is correct! What is the population mean of his homework grades? Round your answer to the nearest tenth. Answer Explanation CORRECT ANSWERS: The population mean is the average calculated on the entire group under study, which in this example is the seven homeworks. To calculate the population mean, add all the grades together, and divide that sum by the number of homeworks. The sum of all the homework grades is 646 and there are 7 homeworks, therefore the population mean of his homework grades is 92.3. FEEDBACK • • • • Content attribution- Opens a dialog Question 20 Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. • $92.3$92.3 That is correct! 37 True False Answer Explanation 40 • • • • Content attribution- Opens a dialog Question 22 Given the following histogram, decide if the data is skewed or symmetrical. A bar graph has a horizontal axis titled Values labeled from 2 to 18 in increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate. 41 That is correct! 42 That is correct! The data are skewed to the left. The data are skewed to the right. The data are symmetric. Answer Explanation Correct answer: The data are symmetric. Note that the histogram appears to be roughly symmetric. So the data are symmetric. FEEDBACK • • • • Content attribution- Opens a dialog Question 23 Of the following pairs of events, which pair has mutually exclusive events? rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll drawing a red card and then drawing a black card with replacement from a standard deck of cards 45 A That is correct! 46 B C Answer Explanation Correct answer: B Remember that the standard deviation tells how spread out the normal distribution is. So a high standard deviation means the graph will be short and spread out. A low standard deviation means the graph will be tall and skinny. The distribution that is the tallest and least spread out is B, so that has the smallest standard deviation. FEEDBACK • • • • Content attribution- Opens a dialog Question 25 A magician appears to be using a biased coin during one of their magic tricks. To find out whether this is true, the alleged unfair coin is flipped twice. The tree diagram below shows the probabilities of the different outcomes. A tree diagram has a root that splits into 2 branches representing the outcomes of an event labeled Upper H and Upper T with probabilities StartFraction 3 Over 8 EndFraction and StartFraction 5 Over 8 EndFraction respectively. Each primary branch splits into 2 secondary branches, labeled Upper H and Upper T. The secondary branches have the following probabilities, with the primary and secondary branches listed first and the probability listed second: Upper H Upper H, StartFraction 3 Over 8 47 EndFraction; Upper H Upper T, StartFraction 5 Over 8 EndFraction; Upper T Upper H, StartFraction 3 Over 8 EndFraction; Upper T Upper T, StartFraction 5 Over 8 EndFraction. 50 Answer: mode=3 cards That is correct! Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears. 3,12,3,11,5,5,3,10,12 Question 4 The dataset below represents bugs found by a software tester in her product during different phases of testing: 88, 84, 81, 94, 91, 98, 98, 200. The measures of central tendency are given below: Mean: 104.25; Median: 92.5; Mode: 98. Identify the outlier and the measure of central tendency that is affected by the outlier. 51 The outlier is 98. The mode is affected by the outlier. The outlier is 98. The mean is affected by the outlier. The outlier is 200. The median is affected by the outlier. The outlier is 200. The mean is affected by the outlier. Question 5 Given the following histogram, decide if the data is skewed or symmetrical. A bar graph has a horizontal axis titled Values labeled from 2 to 18 in increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate. That is correct! 52 That is correct! The data are skewed to the left. The data are skewed to the right. The data are symmetric. 55 That is correct! has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker plot above the class label D has the following five-number summary: 2, 63, 77, 92, and 138. All values are approximate. A B C D Question 8 The box-and-whisker plot shows the number of books read by history students during the last school year. A box and whisker plot with minimum 4, first quartile 6, median 8, third quartile 10, and maximum 15 What is the range of the data? That is correct! Answer: 11 Question 9 A random sample of house sizes in major city has a sample mean of x¯=1204.9 sq ft and sample standard deviation of s=124.6 sq ft. Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 955.7and 1454.1 sq ft. Round your answer to the nearest whole number (percent). 56 That is correct! Answer: 95% Question 10 57 That is correct! That is correct! Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. True False Question 11 Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level. We expect that 416 of every 500 coin tosses will result in heads. At the 0.01 level of significance, the coin is likely not a fair coin. There is certainty that the coin is not a fair coin. The results are not statistically significant at the 0.05 level of significance. Question 12 A spinner contains the numbers 1 through 80. What is the probability that the spinner will land on a number that is not a multiple of 11? • Give your answer in fraction form. 60 Male Female Tota l Orange 12 50 62 Green 2 73 78 Total 17 123 140 That is correct! Answer: 5/17 Question 16 Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked them whether or not they had a fear of flying and whether or not they had a fear of 61 That is correct! heights. The data are shown in the contingency table below. What is the relative risk of being afraid of heights for those who are afraid of flying? Round your answer to two decimal places. Afraid of heights Not afraid of heights Total Afraid of flying 76 33 109 Not afraid of flying 82 370 452 Total 158 403 561 Answer: 3.84 Question 17 Which of the following frequency tables show a skewed data set? Select all answers that apply. That is correct! Value Frequency 5 1 6 2 7 10 62 8 11 9 17 10 17 11 15 12 12 13 7 14 7 15 0 16 1 Value Frequency 5 1 65 That is correct! That is correct! Question 19 The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: 6, 3, 14, 11, 14, 6 • Round the final answer to one decimal place. Answer: Variance = 18 Question 20 A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216 of the 374 residents sampled from urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 0.03. What is the correct interpretation of this calculation? More people from rural areas want the defending champions to win the game. Exactly 216 out of every 374 urban residents want the defending champions to win the game. The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. Answer: 92.3 That is correct! 66 That is correct! The data is not statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. Question 21 Find the mode of the following amounts (in thousands of dollars) in savings accounts of randomly selected people aged 25-30. 8,6,8,7,2,2,2,4,4,4,4,7 67 Answer: Interquartile range is 10 That is correct! Question 22 A deck of cards contains red cards numbered 1,2,3,4,5, blue cards numbered 1,2,3,4,5,6,7,8 and green cards numbered 1,2,3,4,5,6,7,8,9,10. If a single card is picked at random, what is the probability that the card is green? • Give your answer as a fraction. • • That is correct! • Answer: 10/23 Question 23 The five-number summary for a set of data is given below. Min Q1 Median Q3 Max 60 6 5 70 7 87 5 What is the interquartile range of the set of data? Answer: Mode = 4 thousands of dollars 70 Min Q1 M edian Q3 Max 3 5 14 15 20 Me dia n Q3 M ax 3 5 9 15 20 Min Q1 Median Q3 Max 3 10 11 17 20 Min Q1 Median Q3 Max 3 6 18 17 20 Min Q1 Median Q3 Max 71 That is correct! 3 6 7 14 20 QUESTION 1 · 1/1 POINTS A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Blue 2 is one of the outcomes in which of the following events?Select all correct answers. • B AND O • • R OR E • • E′ • • B′ • • R AND E • • O′ • • B AND E • 72 Answer Explanation Correct answer: 75 That's not right. • • • • Content attribution- Opens a dialog QUESTION 3 · 0/1 POINTS If the probability that a randomly chosen college student takes statistics is 0.41, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal. Answer Explanation Correct answers: By the complement rule, the probability of NOT A is 1−P(A). Therefore, the probability that a randomly chosen college student does not take statistics is 1−0.41=0.59. FEEDBACK • • • • Content attribution- Opens a dialog $$.86 • $0.59$0.59 76 QUESTION 4 · 1/1 POINTS 77 $$.16 That's not right. A deck of cards contains RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is picked at random, what is the probability that the card is RED? 812 212 912 312 1012 412 Answer Explanation Correct answer: 312 Because there are 3 red cards, and 12 cards total in the deck, the probability is 312. FEEDBACK • • • • Content attribution- Opens a dialog QUESTION 5 · 0/1 POINTS If A and B are independent events with P(A)=0.6 and P(B)=0.2, find That is correct! 80 Independent events are events in which the knowledge of one event occurring has no effect on the chance of the other event occurring. In this case, each event has the same chance of occurring whether or not the other event occurs. FEEDBACK • • 81 $$.2 That's not right. • • Content attribution- Opens a dialog QUESTION 7 · 0/1 POINTS If A and B are events with P(A)=0.6, P(A OR B)=0.98, and P(A AND B)=0.12, find P(B). Answer Explanation Correct answers: First, it is helpful to write down the addition rule for probabilities: P(A OR B)=P(A)+P(B)−P(A AND B) Now, rearranging this, we find that P(B)=P(A OR B)+P(A AND B)−P(A) Plugging in the known values, we find FEEDBACK P(B)=0.98+0.12−0.6=0.5 • • • • Content attribution- Opens a dialog • $0.5$0.5 82 QUESTION 8 · 1/1 POINTS 85 $$.32 That's not right. P(A AND B)=P(A)P(B) So, plugging in the values we are given, we find that FEEDBACK P(A AND B)=(0.8)(0.3)=0.24 • • • • Content attribution- Opens a dialog QUESTION 10 · 0/1 POINTS Given that P(B|A)=0.76 and P(A)=0.41, what is P(B AND A)? Round to three decimal places. Answer Explanation Correct answers: Remember the multiplication rule for conditional probability: P(B AND A)=P(B|A)P(A) So, plugging in the values that we know, we find FEEDBACK • $0.312$0.312 86 P(B AND A)=(0.76)(0.41)≈0.312 • • • • Content attribution- Opens a dialog 87 $$a1=13, a2=13, a3=23 That is correct! QUESTION 11 · 1/1 POINTS An event is . the set of all possible outcomes of an experiment a subset of the set of all outcomes of an experiment one specific execution of an experiment a planned activity carried out under controlled conditions Answer Explanation Correct answer: a subset of the set of all outcomes of an experiment An event is defined as a subset of the set of all outcomes of an experiment. FEEDBACK • • • • Content attribution- Opens a dialog QUESTION 12 · 1/1 POINTS Write the first three terms of the sequence whose general term is an=n!3n. That is correct! 90 QUESTION 14 · 1/1 POINTS Let E be the event that a randomly chosen person exercises. Let D be the event that a randomly chosen person is on a diet. Identify the answer which expresses the following with correct notation: Of all the people who exercise, the probability that a randomly chosen person is on a diet. P(D) AND P(E) P(E AND D) P(E|D) P(D|E) Answer Explanation Correct answer: P ( D|E ) Remember that in general, P ( A|B ) is read as "The probability of A given B," or equivalently, as "Of all the times B occurs, the probability that A occurs also." So in this case, the phrase "Of all the people who exercise" can be rephrased to mean "Given that a person exercises," so the correct answer is P(D|E) . FEEDBACK • • • • Content attribution- Opens a dialog QUESTION 15 · That is correct! 91 1/1 POINTS Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs are mutually exclusive. 92 That is correct! P(A)P(B)P(C)=0.26=0.5=0.45P(A|B)P(B|C)P(C| A)=0.26=0=0.26 Select all correct answers. • B and C are independent • • A and C are mutually exclusive • • A and B are independent • • A and C are independent • • B and C are mutually exclusive • • A and B are mutually exclusive • Answer Explanation Correct answer: Note that P(A|B)=P(A) , so A and B are independent. Also, P(B|C)=0 , so B and C are mutually exclusive. A and B are independent B and C are mutually exclusive