Relative position measurements

Question 1

1) The weight of a group of Nursing students follows a normal distribution, with a mean of 148 pounds and a standard deviation of 22 pounds. Using the rule of thumb, what is the approximate percentage of students between: a) 104 and 192 pounds, b) 82 and 214 pounds?

Question #2

1) The mean height of the men is 69 inches and its standard deviation is three (3) inches. Carlos is 65 inches tall (Triola, 2004). Answer:

a) What is the difference between Carlos' height and the mean? b) Approximately how many standard deviations from the mean is Carlos's height? Use the empirical rule to answer this question. c) Convert Carlos's height to a Z-score. d) If we consider that the "common" heights are those that correspond to Z scores between -2 and 2, is Carlos' height common or unusual?

Question #3

1) With a mean of 98.20 and a standard deviation of 0.62, convert the following temperatures to Z-scores.

a) 97.52 b) 98.60 c) 98.10

Question #4

1) Which is relatively better: a score of 88 on a Psychology test or a score of 45 on an Economics test? Psychology test scores have a mean of 92 and a standard deviation of 10. Economics test scores have a mean of 57 and a standard deviation of 5. Use the measures of relative standing to answer this exercise (Z Score) (Triola, 2004).

Question #5

a) What is the highest relative score of the three (3) scores below? Use the Z value to answer. a score of 194 on a test with a mean of 128 and a standard deviation of 34 b) a score of 91 on a test with a mean of 86 and a standard deviation of 18 c) a score of 17 on a test with a mean of 15 and a standard deviation of 5

Question #6

1) In a time study conducted at a manufacturing plant, the time to make a specified operation was measured for each of 40 workers. The mean and standard deviation were found to be 14.8 and 1.6, respectively. Describe the sample data using the empirical rule (Mendenhall et al., 2015).

Question #7

1) The mean and variance of a sample of 25 data are 78 and 100, respectively. Use Tchebyshev's theorem to describe the distribution of the data.

Question #8

1) The data below is the weight (in pounds) of 15 packages of ground beef in Supermax supermarket refrigerators: 1.28, .90, 1.29, 1.15, .93, 1.18, .89, 1.12, 2.33, 1.94, 2.14, 2.6, 1.11, 1.9, 1.2 (Mendenhall et al., 2015). a) Construct a stem-and-leaf plot to show the distribution of these weights. b) Find the mean and standard deviation of the data set. c) Find the percentage of measurements in the intervals