MATH 1131 3.00 A S1 Assignment 1 Total marks = 65 Question 1: Water quality ratings (A, B, C, D, F) which reflect the risk of getting sick from swimming at any particular one of 36 Southern California beaches, are given in the following list: A B F F A A A A B A A C F C A D D F A C C A A B A A A A A A ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m A A A D D A (a) (4 marks). Summarize the given ratings by constructing a relative frequency distribution and a bar chart. (b) (2 marks). Assuming that an A means little risk of getting sick, does it appear that the majority of beaches in Southern California are safe? On what information do you base your answer? (c) (2 marks). Would it be appropriate to construct a dotplot for these data? Why or why not? 24 8 24 34 24 26 14 30 sh Th is Question 2: The time (in months) to the first electrical malfunction of a pacemaker was recorded for a sample of 89 heart patients: 20 16 26 18 10 20 18 22 16 12 28 20 14 6 24 24 32 24 18 22 16 14 22 22 14 14 14 24 22 16 28 32 22 20 10 26 24 18 24 2 18 12 18 22 24 30 12 14 24 2 20 18 34 24 16 6 18 24 16 26 6 18 12 12 28 6 24 10 20 18 12 20 16 22 20 22 16 8 22 10 28 (a) (1 mark). Construct a relative frequency distribution for this data using the following class intervals 0 to < 6, 6 to < 12, and so on. 1 https://www.coursehero.com/file/7637737/a1/ (b) (3 marks). Draw the corresponding histogram and describe its shape. (c) (1 mark). If the pacemaker must be replaced as soon as the first electrical malfunction occurs, approximately what proportion require replacement within less than 2 years of implantation? (d) (2 marks). Using only the relative frequency distribution and not the raw data, what is the approximate time at which about 50% of pacemakers fail? ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Question 3: Data on the total tobacco exposure time (in seconds) for G-rated animated films with tobacco use released between 1937 and 1997 produced by Walt Disney, Inc. are as follows: 223 176 548 37 158 51 299 37 11 165 74 92 6 23 206 9 Similar data for G-rated animated films with tobacco use produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox are as follows: 205 162 6 1 117 5 91 155 24 55 17 (a) (4 marks). Construct a back-to-back stem-and-leaf plot to compare the two exposure-time distributions. Use hundreds for stems and tens (truncated) for leaves. Divide each stem into a \"Low\" and \"High\" part. Th is (b) (4 marks). Compare the two exposure-time distributions with respect to shape, centre, spread and outliers. Question 4: sh (a) (2 marks). A sample consisting of four pieces of luggage was selected from among those checked at an airline counter, yielding the following data on x = weight (in pounds): x1 = 33.5, x2 = 27.3, 2 https://www.coursehero.com/file/7637737/a1/ x3 = 36.7, x4 = 30.5 Suppose that one more piece is selected; denote its weight by x5 . Find a value of x5 , other than 32, such that x = sample median. (b) (5 marks). An instructor has graded 19 exam papers submitted by students in a class of 20 students, and the mean mark so far is 70. (The maximum possible mark is 100.) How high would the mark on the last paper have to be to raise the class mean by 1 mark? By 2 marks? ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Question 5: The following data are the ages (in years) at diagnosis for 20 patients under treatment for meningitis: 18 18 25 20 18 18 19 23 20 69 18 21 18 20 18 19 28 17 18 18 (a) (6 marks). Calculate and interpret the values of the sample mean, variance, and standard deviation. (b) (4 marks). Compute the 10% trimmed mean and the sample median. Why might you recommend either one of these two statistics as measures of centre rather than the sample mean? (c) (3 marks). Compute the upper quartile, the lower quartile, and the interquartile range. (d) (13 marks). Illustrate the center, spread, and symmetry or skewness of this data using a horizontal modified boxplot. Question 6: Suppose that the distribution of marks on an exam is closely described by a normal curve with a mean of 65. The 84th percentile of this distribution is 75. Th is (a) (2 marks). What is the 16th percentile? (b) (2 marks). What is the approximate value of the standard deviation of exam marks? sh (c) (1 mark). What z score is associated with an exam mark of 50? (d) (2 marks). What percentile corresponds to an exam mark of 85? (e) (2 marks). Do you think there were many marks below 35? Explain. 3 https://www.coursehero.com/file/7637737/a1/ Powered by TCPDF (www.tcpdf.org)