MATH 225N Week 4 Quiz and Answers (Spring Term) REVISED VERSION WITH CORRECT ANSWERS (2020/2021)

Brayden tosses a coin 500 Of those 500times, 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.

2. Question: Suppose X∼N(11,0.5), and x=12. Find and interpret the z-score of the standardized normal random variable.

3. Question: A normal distribution is observed from the times to complete an obstacle course. The mean is 69seconds and the standard deviation is 6 Using the  Empirical Rule, what is the probability that a randomly selected finishing time is greater than 87 seconds?……. Provide the final answer as a percent rounded to two decimal places.

4. Question: 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: 25; Median: 92.5; Mode: 98. Identify the outlier and the measure of central tendency that is affected by the outlier.

5. Question: 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.

6. Question: The following data set represents the ages of all seven grandchildren in a family….. 4, 5, 11, 12, 11, 8, 5….. If the variance of the ages is 9.7, what is the standard deviation?…. Round the final answer to one decimal place.

7. Question: 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

8. Question: 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

9. Question: Given the following list of data, what is the five-number summary?
2, 2, 2, 3, 3, 4, 4, 5, 6, 10, 11, 11, 13, 13, 14

10. Question: 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?

11. Question: The five number summary for a set of data is given below.

Min     Q1       Median           Q3       Max

61        69        72                    79        86

Using the interquartile range, which of the following are outliers? Select all correct answers.

12. Question: 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.

13. Question: Given the following list of the number of voicemails each employee received at an office during the last workday, find the median…… 11,4,21,8,7,2,3,17,26,4,6

14. Question: Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains……. 

15. Question: Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?….. Four horizontal box-and-whisker plots share a vertical axis with the classes D, C, B, and A and a horizontal axis from 0 to 120 in increments of 20. The box-and-whisker plot above the class label A has the following five-number summary: 44, 69, 77, 82, and 112. The box-and-whisker plot above the class label B has the following five-number summary: 19, 64, 78, 87, and 121. The box-and-whisker plot above the class label C 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.

16. Question: Researchers want to study whether or not a fear of flying is … 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 … 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

17. Question: Diana is packing a lunch that will include an orange. Diana has 3navel 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. 

18. Question: A spinner contains the numbers 1through 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.

19. Question: A student wants to know his average homework grade for the first half of his math class. There were 7homeworks in the first half of the class, and his grades out of 100 are given by…… 100,90,95,89,92,85,95.

What is the population mean of his homework grades? Round your answer to the nearest tenth.

20. Question: 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.

21. Question: A group of 140students at an elementary school were asked if they prefer the color orange to the color green. The results are shown in the table below. Given that a randomly selected survey participant is a male, what is the probability that this student prefers the color green?

22. Question: 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 … 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.

23. Question: Of the following pairs of events, which pair has mutually exclusive events?

24. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation……. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is short and the most spread out, curve Upper B is tall and the least spread out, and curve C is farther to the left than A.

25. Question: 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 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…… Use the diagram to find the probability of getting one head and one tail (in either order)……. Provide the final answer as a fraction.