1. Determine whether the following variables are categorical or quantitative. (a) Number of laps a subject can swim (b) Color of a randomly selected beetle (c) Birth weight (d) Hometown (e) Life of a battery measured in hours 2. The data below represents measurements of the weight of a candy bar in decagrams. (a) Create a histogram with an appropriate number of intervals which shows the distributions of this data. 33 30 25 60 63 43 26 35 62 44 45 70 14 33 54 31 33 44 23 47 54 56 43 38 57 64 22 42 13 44 (b) Describe the shape of this data. Is the distribution symmetric? Are there any outliers? 3. A study is conducted where five colored sticky pads (red, orange, yellow, green, and purple) are placed in a field and after some time, the insects which have been trapped on each pad is counted : The results of the study are displayed in the table below. Create a pie-chart and a bargraph to show the distribution Red Orange Yellow Green Purple of this data. 23 45 76 34 10 4. Compute the mean, median, Q1 , Q3 and the standard deviation for the following observations:4, 5 ,7 , 12 ,5, 8. 5. If the mean of 20 observations is 32, then what is the sum of all of the observations? 6. A student received scores of 92, 83, and 71 on three quizzes. What is the lowest score that the student can get on the next test, which is out of 200, to achieve a mean of at least 80? 7. If your scores of the first four exams are 98, 100, 90 and 97, what do you need to make on the next exam for your overall mean to be at least 90? 8. A student received the following grades on quizzes in a history course: 80, 88, 75, 93, 79, 95, 75, and 96. Find the mean, and median, and the first and second quartiles of this data. Also compute the standard deviation. 9. Suppose that the weight of a molar is normal with mean 30mg and standard deviation 4mg. What portion of molars weigh on average will more than 31mg? 10. To make a knife, a steel blank has to be cut so that it is longer than 7 inches but shorter than 7.3 inches. Suppose the length of steel blanks which are manufactured follows a normal distribution with mean 7.25 inches and a standard deviation of 18 of an inch. What portion of the blanks manufactured on average will meet these specifications? 11. The wingspan of a falcon in feet follows a N(3.3,.1) distribution. What portion of observations of the wingspan of falcons do you expect to find between 3.1 and 3.5 feet? 12. The wingspan of a falcon in feet follows a N(3.3,.1) distribution. How large must a bird’s wingspan be in order to place it in the top 10% of all falcons? 13. A circus is recruiting chimpanzees for a show, and they want the chimpanzees to be either really tall, or really short. The heights of monkeys follow a normal distribution with mean 4 feet and standard deviation 6 inches. If the circus purchases a whole barrel of chimps, what portion do you expect to have heights larger than 5 feet and smaller than 3 feet 7 inches? 14. The data below relates the weights of fruitflys (in micro grams) to the number Fruit Fly Weight Number of offspring 1 22 43 2 26 47 3 19 40 of offspring they produce. 4 17 38 5 27 50 6 21 42 7 26 46 (a) Create a scatter plot for this data. (b) Does the data exhibit a positive or negative association? (c) What is an estimate for the correlation coefficient for this data? 15. Suppose that the heights and shoe sizes are measured of a sample of men from the University. It is found that the mean height of this sample is 6 feet with a standard deviation of .5 feet, and that the mean shoe size is a 10 with a standard deviation of 1. Suppose also that the correlation coefficient is computed between the two samples and is .75. (a) Compute the least squares regression line for this data set. (b) Suppose that Kyle, a university student, wears a size 10.5 shoe. What is the best prediction for his height?