The owner of a popular barber shop in stanbul is anxious about reducing the total time a customer spends (i.e waiting to be served plus time served) in the barber shop. They randomly select six customers each day and find the total time they spent in the shop. Using these 6 observations they find the sample mean and range R. These observations are repeated for 50 days. The summary data for these 50 samples are given as:

Mean of the 50 sample means = 50 and the mean of 50 sample Ranges = 6.

(a)Construct the Mean X- and R- chart upper and lower control limits.

(b)Find the percentage of customers who will not have spent more than 60 minutes in the shop, assuming that time spend in the barber shop is distributed normally.

(c)The owner of the barber shop, reduces the average time spent in shop to 40 minutes by employing more workers. With this new average time what proportion of customers will have to stay in the shop longer than 45 minutes?

The following data are ages (in years) of 10 students

20, 20, 20, 20, 20, 20, 20, 20, 20, 20

Find the standard deviation. Comment on your answer.

10 Consider the following two data sets:

Data set I: 13, 25, 27, 15

Data set II: 10, 15, 30, 25

Find the mean and the standard deviations for each data set of

the two data sets above. Comment on your answer.

11 Fatima is currently taking college economics. The instructor

often gives quizzes. On the past five quizzes, Fatima got the

following scores

5, 19, 2, 13, 10

Find the range for her scores.

12 The owner of a small manufacturing plant employs six people.

As part of their personal file, she asked each one to record to

the nearest one-tenth of a mile the distance they travel one

way from home to work. The six distances are listed below.

2.3, 5.5, 1.1, 4.3, 6.4, 3.5

Find the range for these data.

13 A class of sixth grade students kept accurate records on the

amount of time they spent playing video games during a one

1. (25 pts.) The class registrations of 50 mechanical engineering students are analyzed. It is found that: *5 students take all three subjects (Dynamics, Statistics, and Fluid Mechanics), Dynamics * 18 students take Dynamics and Statistics, * 9 students take Dynamics and Fluid Mechanics, *7 students take Statistics and Fluid Mechanics, * 29 students take Dynamics, * 15 students take Fluid Mechanics, * 1 student takes none of the three. Statistics Fluid (1) How many students take only Statistics? (2) What is the probability that a student selected at random takes all three, given she/he takes Statistics? (3) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all three courses? (4) n(Statistics ( Dynamics) = ? (5) n Statistics ~ Fluid Dynamics) = ?An engineering statistics class has 40 students; 60% are electrical engineering majors, 10% are industrial engineering majors, and 30% are mechanical engineering majors. A sample of four students is selected ran- domly without replacement for a project team. Let X and Y denote the number of industrial and mechanical engineering majors in the sample, respectively. (a) Determine the joint PDF of X and Y. (b) Determine the marginal PDF of X. (0) Determine the expected value of X. At University of West Georgia, 45% of the students take a Statistics class, 39% of the students take a Geography course, and 30% of the students take both Statistics and Geography classes. What is the probability that a student take either Statistics or a Geography course? Write your answer as a decimal. 0.36 O 0.24 0.54 0.45Q3. A construction company includes 6 civil engineers, 5 mechanical engineers and 4 electrical engineers. A committee responsible for overseeing the implementation of a construction project must he formed consisting of 3 civil, 2 mechanical and 2 electrical engineers. Determine the number of possible ways to form this committee for the following cases: (12 Marks) A. Any civil, mechanical and electrical engineers can be selected to form this committee. B. One particular civil engineer and one particular electrical engineer should be selected as they have the necessary qualications. C. One particular mechanical engineer should not be selected as there is a shortage in the relevant experience