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Statistics Homework Copy 2.3 A shirt inspector at a clothing factory categorized the last 500 defects as: 67–missing button, 153–bad seam, 258–improperly sized, 22–fabric flaw. Construct a Pareto diagram for this information. 2.7 The U.S. Women’s Olympic Soccer Team had a great year in 2008. One way to describe the players on that team is by their individual heights. Height (in) 70 68 65 64 68 66 66 67 68 68 67 65 65 66 64 69 66 65 a. Construct an ungrouped frequency distribution for the heights. b. Construct a frequency histogram of this distribution. c. Prepare a relative frequency distribution for this same data. d. What percentage of the team is at least 5 ft 6 in tall? 2.24 The U.S. Geological Survey collected atmospheric deposition data in the Rocky Mountains. Part of the sampling process was to determine the concentration of ammonium ions (in percentages). Here are the results from the 52 samples: 2.9 4.1 2.7 3.5 1.4 5.6 13.3 3.9 4.0 2.9 7.0 4.2 4.9 4.6 3.5 3.7 3.3 5.7 3.2 4.2 4.4 6.5 3.1 5.2 2.6 2.4 5.2 4.8 4.8 3.9 3.7 2.8 4.8 2.7 4.2 2.9 2.8 3.4 4.0 4.6 3.0 2.3 4.4 3.1 5.5 4.1 4.5 4.6 4.7 3.6 2.6 4.0 a. Find Q1 b. Find Q2 c. Find Q3 d. Find the midquartile f.. Find the 5-number summary g. Draw the box-and-whiskers display 2.29 The mean lifetime of a certain tire is 30,000 miles and the standard deviation is 2,500 miles. a. If we assume the mileages are normally distributed, approximately what percentage of all such tires will last between 22,500 and 37,500 miles? 3.9 An experimental psychologist asserts that the older a child is, the fewer irrelevant answers he or she will give during a controlled experiment. To investigate this claim, the following data were collected. Draw a scatter diagram. (Retain this solution to use in Exercise 3.19) Age (x) 2 4 5 6 6 7 9 9 10 12 Irrelevant Answers (y) 12 13 9 7 12 8 6 9 7 5 3.16 Estimate the correlation coefficient for each of the following: 3.19 a. Use the scatter diagram you drew in Exercise 3.9 to estimate r for the sample data on the number of irrelevant answers and the child’s age. a. Calculate r. 4.4 The table here shows the average number of births per day in the United States as reported by the CDC. Day Number Sunday 7,563 Monday 11,733 Tuesday 13,001 Wednesday 12,598 Thursday 12,514 Friday 12,396 Saturday 8,605 Sunday 78,410 Based on this information, what is the probability that one baby identified at random was: a. Born on a Monday? b. Born on a weekend? c. Born on a Tuesday or Wednesday? d. Born on a Wednesday, Thursday, or Friday? 4.12 Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster. Gender Female Male Satisfied 80 55 Not Satisfied 120 45 One viewer is to be randomly selected from those surveyed. a. Find P(satisfied) b. Find P(satisfied | female) c. Find P(satisfied | male) 5.44 A January 2005 survey of bikers, commissioned by the Progressive Group of Insurance Companies, showed that 40% of bikers have body art, such as tattoos and piercings. A group of 10 bikers are in the process of buying motorcycle insurance. a. What is the probability that none of the 10 has any body art? b. What is the probability that exactly 3 have some body art? c. What is the probability that at least 4 have some body art? d. What is the probability that no more than 2 have some body art? 6.3 Find the area under the normal curve that lies to the left of the following z values. a. z = –1.30 b. z = –2.56 c. z = –3.20 d. z = –0.64 6.6 Find the following areas under the standard normal curve. a. to the right of z = –0.47, P(z > –0.47) b. to the right of z = –1.01, P(z > –1.01) c. to the right of z = –3.39, P(z > –3.39) 6.14 Find the area under the normal curve that lies between the following pairs of z-values: a. z = –1.20 to z = –0.22 b. z = –1.75 to z = –1.54 c. z = 1.30 to z = 2.58 d. z = 0.35 to z = 3.50 Assume you want to bet some money on a horse in a certain horse race. After a careful analysis of the times made by each horse running the distance, and the number of times each horse has run and won a similar contest, you find out the choices are reduced to three. The times (in minutes) made by each of the horses are shown below. Horse A 1.95 2.00 2.05 2.15 2.19 2.25 2.26 2.35 x = 2.15 Horse B 1.95 2.10 2.13 2.14 2.16 2.18 2.19 2.35 x = 2.15 Horse C 2.08 2.09 2.10 2.10 2.11 2.11 2.13 2.48 x = 2.15 We want to choose the horse that is more consistent in running a time near the mean! 1. Use the graphic calculator to fill out the table below. Minimum Q1 Median Q3 Maximum Range Q3-Q1 Sx Horse A Horse B Horse C 2. In the TI-83 Plus or Excel, construct a Box-and-Whisker chart for each data set. Transfer the charts to the computer and copy and paste them in Word. Print the resultant graph and attach. 3. Comparing the boxplots and the information in the table, which horse is more consistent in running the distance in a time near the mean? Explain. 4. Assume you bet for a horse in a game, what are the factors that you will consider to pick a horse. Write half of a page long about these factors. Use the table to solve the problems. Student Status/Gender Male Female Total Never Married 45 55 100 Married 30 50 80 Widowed 25 32 57 Divorced 35 33 68 Separated 20 25 45 Total 155 195 350 1. Find the probability that a student is Divorced. a. 0.2857 b. 0.1629 c. 0.1943 d. 0.009 2. Find the probability that a student is Widowed and Female. a. 0.1053 b. 0.0914 c. 0.10 d. 0.0571 3. Find the probability that a student is Widowed or Female a. 0.6286 b. 0.5748 c. 0.1242 d. 0.7237 4. Find the probability that a student is Divorced given that is Male. a. 0.1692 b. 0.2258 c. 0.2903 d. 0.0901 5. The Red Sox win a game with probability 0.62 If the Red Sox play 3 games. Find the Probability that they win all 3 games a. 0.1477 b. 0.2987 c. 0.2383 d. 0.0549 The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days. 7. What is the z-score for 240 days? Use formula: Z= ?−µσ a. 1.62 b. -1.63 c. 1.63 d. -1.62 8. What is the probability that a pregnancy lasts less than 240 days? That is P (x < 240) a. about 0.9500 b. about 0.0500 c. about 0.1205 d. about 0.0650 9. what is the probability that pregnancies last between 240 and 270 days? a. about 0.55 b. about 0.67 c. about 0.45 d. about 0.19 240)="" a.="" about="" 0.9500="" b.="" about="" 0.0500="" c.="" about="" 0.1205="" d.="" about="" 0.0650="" 9.="" what="" is="" the="" probability="" that="" pregnancies="" last="" between="" 240="" and="" 270="" days?="" a.="" about="" 0.55="" b.="" about="" 0.67="" c.="" about="" 0.45="" d.="" about="">