Practice Problems - Topic 2

docx

School

Carleton University *

*We aren’t endorsed by this school

Course

3127

Subject

Statistics

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by AmbassadorCrownFrog10

Practice Problems – Topic 2 Note: Unless the problem specifically states that you can use Minitab or Excel, assume that you cannot and complete the problem by hand and calculator. 1. You may use Minitab or Excel for this problem. The following data represent the number of books read by 42 grade 6 students between September and June: 14 9 21 19 35 26 23 21 19 40 4 24 44 32 12 6 7 18 38 18 1 48 20 11 8 24 17 15 13 7 28 16 6 9 31 15 25 18 32 33 26 26 a. Determine the mean and standard deviation of the data. (2.4) b. What is the median number of books read? (2.4) c. Make a histogram of the data. Does it look normally distributed? (2.5) d. Make a boxplot of the data. Are there any outliers? (2.5) 2. Stephanie has marks of 80%, 72%, 68%, 83%, 70%, 62% and 81% in 7 of her subjects. What percentage does she need in her 8’th course to have an average of 75%? (2.4) 3. A set of data has mean 43.5 and standard deviation 2.5. Within what symmetric limits around the mean will 75% of the data lie? (2.3) 4. The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kg/cm 2 and a standard deviation of 100 kg/cm 2 . (2.3) a. What is the probability that a sample’s strength is less than 6250 kg/cm 2 ? b. What strength is exceeded by 95% of the samples? 5. PVC pipe is manufactured with a mean diameter of 1.010 cm and a standard deviation of 0.003 cm. Find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 cm and less than 1.012 cm. (2.3) 6. A normal population has mean 100 and variance 25. How large must the random sample be if we want the standard error of the sample mean to be 1.5? (2.3) 7. The following are recorded benzene boiling points measured after distillation in an aromatics plant: 80.1 80.5 79.7 79.9 80.3 80.2 Questions 1-3 are adapted from Statistics & Data, Coles Notes Study Guide, 2010. Questions 4-7 are adapted from Applied Statistics and Probability for Engineers, Montgomery and Runger, 4’ed., Wiley, 2007. 1

Calculate the sample mean, the sample variance, and the sample standard deviation. (2.4) 8. You may use Minitab or Excel for this problem. A CHG3337 student recorded the time in minutes that it too her to walk to the University of Ottawa took. The times in minutes are in the following table. The data is available on the CHG3337 Brightspace in the Practice Problems 1 folder in the Minitab worksheet PP1Q09.MTW. W e e k M o n T u e s W e d T h u r s F r i 1 2 3 . 7 2 4 2 0 . 9 2 5 . 1 2 4 . 6 2 2 0 . 9 2 3 . 4 2 0 2 1 . 6 2 2 . 3 3 2 4 . 3 2 7 . 6 2 8 . 9 2 9 . 2 2 3 . 5 4 2 4 . 3 2 4 . 5 2 7 2 7 . 2 2 7 . 6 5 2 0 . 3 2 0 . 9 2 3 . 4 3 7 . 3 2 3 . 1 6 2 8 2 6 2 5 . 4 2 3 . 4 3 0 7 2 4 . 4 2 7 2 3 . 7 2 2 . 1 2 4 . 3 8 2 2 . 6 2 6 . 5 2 1 . 4 2 4 . 5 2 5 . 1 9 2 6 . 7 2 3 . 9 2 5 . 8 2 2 2 2 . 3 1 0 2 4 . 2 8 . 2 0 . 2 4 . 2 0 . Questions 1-3 are adapted from Statistics & Data, Coles Notes Study Guide, 2010. Questions 4-7 are adapted from Applied Statistics and Probability for Engineers, Montgomery and Runger, 4’ed., Wiley, 2007. 2

7 6 9 7 4 a) Plot a histogram for these data, and calculate the sample mean and the sample standard deviation of all 50 observations. (Hint: Use the Stack Columns feature under the Data menu of Minitab.) (2.5) b) Calculate the mean time for each week and the standard error for the mean (the standard deviation of the week means) (Hint: Use the Row Statistics feature under the Calc menu of Minitab). Estimate the overall (individual) standard deviation using the standard error for the mean (Hint: Use the Central Limit Theorem). How does it compare with the standard deviation you determined in part (a)? (2.6) 9. If a random variable has a normal distribution with mean 50 and standard deviation 5, what is the probability that it assumes a value: (2.3) a) Between 44.4 and 58.6? b) Less than 38.5 or greater than 52.5? 10. What is the probability of finding at least one nonconforming unit from a sample of 10 units where the probability of a nonconforming unit is 0.05? What is the probability of finding exactly two nonconforming units? (2.2) 11. In an experiment with six (6) experimental factors, how many ways are there for three (3) factors to combine to produce an effect on the experimental response? (2.2) Questions 1-3 are adapted from Statistics & Data, Coles Notes Study Guide, 2010. Questions 4-7 are adapted from Applied Statistics and Probability for Engineers, Montgomery and Runger, 4’ed., Wiley, 2007. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version