Statistics

MSB 701 Mid-Term – SP 21 Professor Masele Kibassa

Please show work to receive credit 1. For 20 points - At the Christina Steel Company (CSC), steel rods are manufactures with a mean length of 25

centimeter (cm). Because of variability in the manufacturing process, the length of the rods are approximately

normally distributed, with a standard deviation of 0.08 centimeter. Please show all calculations and drawing…

a. What is the probability that a randomly selected rod has a length longer than 26.03 cm? (4 points)

b. What is the probability that a randomly selected rod has a length shorter than 24 cm? (4 points)

c. Any rods not between the lengths of 24.85 cm and 25. 08cm will be discarded. What is the probability that a

randomly selected rod will be discarded? (4 points)

d. Trudy Manufacturing Inc. (TM), just informed CSC that they will only order rods within the middle 85% of all

rods. You, as the Product Analyst at TM, are tasked to determine the acceptable lengths of these rods. (4 points)

e. DeRosa Mining Company (DMC), another client of CSC, just informed them that they will only seek to order rods

within the top 11 %. What is the cutoff length? (4 points)

For 15 points - Please show all calculations and you can use calculations done in other parts to avoid repetitions 2. Consider a computer system with Poisson job-arrival stream at an average of 13 jobs per 4 minutes. Determine the

probability that in any one-minute interval there will be:

a. No jobs

b. Exactly 4 jobs

c. At most 3 jobs

d. At least 3 jobs

e. Between 1 to 5 jobs inclusive

3. For 20 points - In Chapter 1, we spoke about how qualitative events can be the main catalyst impacting quantitative

measurements. In details (use the entire page), talk about an industry that has been quantitatively affected by the current event dominating our society now and elaborate on it. Give concrete examples and

explanations.

For 15 points - Please show all calculations and you can use calculations done in other parts to avoid repetitions 4. Sixty-two percent of adults would still consider a car brand despite product/safety recalls. You randomly select eight

adults. Use binomial distribution to find the probability that the number of adults who would still consider a car brand

despite product/safety recalls is:

f. Exactly 3

g. At most 3

h. At least 3

i. Between 2 and 5, inclusive

5. Given the following data (for 30 points). Show all computations; you may use excel to verify your answer only and the second part of e.

X= additional number of studying hours since last exam 4 3 8 7 8 11 14

Y= Grade improvement since last exam 5 5 9 8 10 13 16

a. Draw a scatter diagram and speculate on the linear relationship between x and y

b. Find the coefficient of correlation and Comment on it. Use the formula learned in class and show all steps and calculations

c. Compute the coefficient of determination and tell us what that means. Use the formula learned in class and show all steps

d. Find the equation of the regression line. Use the formula learned in class and show all steps

e. Use the regression model to compute the value of to find the value of Y if x = 10.5 (Show work); is this a case

of “garbage in garbage out” and why? use alpha = 0.05 (you can use Excel to help you with the decision)?