Sophia Intro to Statistics Unit 2 Milestone 2

1 Select the statement that correctly describes a normal distribution.  It is a positively skewed distribution, as the extreme values are greater than the median.  It is a symmetric distribution, as the mean and the median are the same.  It is a uniform distribution, as all of the values have equal frequency.  It is a negatively skewed distribution, as the extreme values are less than the median. RATIONALE A normal distribution is a bell-shaped and symmetric distribution. So it has a smooth peak, which tells us the mean and median are the same. CONCEPT Normal Distribution 2 At Priscilla's school, the final grade for her Calculus course is weighted as follows:  Tests: 50%  Quizzes: 30%  Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?  73.4%  69%  77.5%  56.1% RATIONALE In order to get the weighted average we use the following formula: CONCEPT Weighted Mean 3 The dot plot below shows the number of songs Carly downloaded over 15 successive weekends What is the greatest number of songs downloaded?  10  8  9  5 RATIONALE The dotplot is a number line that shows the number of items at each value, which is designated with an X. So the largest value we can see is at 10. CONCEPT Dot Plots 4 The manager went over the sales of mobile phones at the store and found that the mean sale was 45, with a standard deviation of 4. On a particular day, 52 mobile phones were sold. What is the z-score of the sale of mobile phones on that day?  28  1.75  -1.75  -28 RATIONALE Recall that the z-score can be calculated with the following formula: The given value is 52 phones, the mean is 45 phones, and the standard deviation is 4 phones. Plug these values in to get the following z-score: This also tells us that 52 is 1.75 z-scores or standard deviations above the mean. CONCEPT Standard Scores and Z-Scores 5 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 21 or higher on the quiz is __________.  32%  18%  68%  16% RATIONALE To get the relative cumulative frequency of 21 or greater, we need to first find the cumulative number of 21 or more. We simply add up any bin that has the number 21 or more, such as the bin that shows scores of 21-25, 2630, 31-35, and 36-40. This would be: To calculate relative cumulative frequency, we will take this cumulative number and divide it by the total number of students. CONCEPT Cumulative Frequency 6 The midterm exam scores obtained by boys and girls in a class are listed in the table below What does the circled section represent?  Twelve boys scored 8 marks on the exam.  Two boys scored between 80 and 89 marks on the exam.  Eight boys scored 12 marks on the exam.  Eight boys scored over 10 marks on the exam. RATIONALE If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to 81 and 82. We can then note that there are two scores from boys between 80 and 89. CONCEPT Stem-and-Leaf Plots 7 The graph in the figure shows the change in the Consumer Price Index over an 11-year period. Which segment of the graph indicates no change in the Consumer Price Index?  H  E  D  A RATIONALE In this graph, a segment that is horizontal would show no change in the consumer price index. This occurs at segment E. CONCEPT Line Charts and Time-Series Diagrams 8 In a survey to rate the customer service department of a company, 300 persons rated their agreement with the statement, "The staff is helpful and courteous." The information was put into a table. Rating Frequenc Strongly Agree 32 Agree 50 Neutral 97 Disagree 53 Strongly Disagree 68 The relative frequency of people who strongly disagree with the statement is __________.  10.7%  40.3%  22.7%  68% RATIONALE To get the relative frequency, we take the frequency of the value and divide it by the total number. So in this case for strongly disagree, the relative frequency would be: CONCEPT Frequency Tables 9 The first quartile (Q1) value from the above box plot is __________.  65  54  40  47 RATIONALE Note the value for Q1 is the left edge of the box, which is 47. CONCEPT Five Number Summary and Boxplots 10 The formula for the standard deviation of a sample is: Select the true statement for the following data set that has a mean of 8: 4, 6, 6, 6, 9, 9, 12, 12 Answer choices are rounded to the hundredths place.  The variance is 7.50 and the standard deviation is 2.98.  The variance is 8.86 and the standard deviation is 2.98.  The variance is 2.98 and the standard deviation is 8.86.  The variance is 8.86 and the standard deviation is 7.50. RATIONALE We can first calculate the variance of the data, , by using the part of the formula under the square root: Next, we can find the standard deviation, , by simply taking the square root of the variance: We can also use the statistical functions in Excel to quickly find the variance and standard deviation. CONCEPT Standard Deviation 11 Which of the following statements is true?  The Central Limit Theorem is applicable only for data sets comprising more than thirty samples.  The Central Limit Theorem is applicable only for data sets comprising exactly thirty samples.  The Central Limit Theorem is applicable only for data sets comprising thirty or more samples.  The Central Limit Theorem is applicable only for data sets comprising less than thirty samples. RATIONALE Recall that the Central Limit Theorem outlines that when the sample size is large, then the distribution of sample means will be approximately normal. For most distributions, the sample size is n ≥ 30, meaning a sample of 30 or more observations is considered a good sample size. CONCEPT Shape of a Sampling Distribution 12 For a class reading competition, the students were asked to read a book. Mike, Jack, and Rayon discussed the numbers of pages they read on the first day. One of them made a graph to represent the data. Who made the graph, and why?  Rayon, because he wanted to make the amount read by each person appear very different.  Mike, because he wanted to accurately show the amount read by each person.  Mike, because he wanted to make the amount read by each person appear reasonably close.  Jack, because he wanted to make it look like he read significantly more than the others. RATIONALE Since there was a competition, the person who most likely made this graph would want to represent themselves favorably. Since Jack has the most pages, it would probably be him. CONCEPT Misleading Graphical Displays 13 Which of the following statements is true?  A standard normal curve has a mean of 0 and a standard deviation of 1.  A standard normal curve has a mean of 1 and a standard deviation of 1.  A standard normal curve has a mean of 0 and a standard deviation of 2.  A standard normal curve has a mean of 1 and a standard deviation of 2. RATIONALE The standard normal distribution is a normal distribution that is centered at 0 and a standard deviation of 1. CONCEPT Standard Normal Distribution 14 Adam graded ten standardized tests with the following scores: 48, 65, 72, 86, 84, 52, 93, 97, 81, 80 Which standardized test score represents the 70th percentile?  84  72  86  65 RATIONALE If we note that there are 10 values, so the 70th percentile can be found with the following calculation: This tells us that we need to find the 7th ordered value. The 7th value is 84. CONCEPT Percentiles 15 Consider this histogram showing the number of students in grade five who have one or more pets What is the difference in the number of students with the most and least numbers of pets?  9  10  2  4 RATIONALE The most number of pets is 10 and there is 1 person who has this many pets. The least number of pets is 1 and there are 5 people with 1 pet. So