Question 1

Suppose that for a call center "ALPHA" want to hire some more staff. A Resume of 351 applicant for a job is received. For this job, it approved 153 applicants initially, rejected 110 outright, and on hold 88 for the future consideration. In the past, this call center has approved 20% of the on hold initial applications of applicants. Let I, R, and H represent the events that an applicant who applies for a job is approved Initially, Rejected outright, and on Hold for a call center need

• Use the data to estimate P(I), P(R), and P(H).
• Are events I and R mutually exclusive? Find P ( I U R)
• Suppose an applicant applies for a job. What is the probability that the applicant will be approved for initially job or be on hold and later got the job in a call center?

Question 2

According to the "ALPHA" company, there employees generally spend more than 55 hours each week working on official duties. The following data show the number of hours worked per week for a sample of 13 IT department and a sample of 11 Accounts department.

IT department:66646465685971646462636658

Accounts department:5760565758595662615859

• What is the third quartile of spending working hours for Accounts department?
• Create a box plot for the number of hours worked for IT department
• Develop a relative frequency distribution and a percent frequency distribution for the above departments
• Calculate the z - score for the above data

Question 3

• Given are the points A = (3,4), B = (4,4), C = (4,3), D = (-3,6), E = (-4,-3), F = (-3,-3). Starting from initial clusters Cluster1 = {A} which contains only the point A and Cluster2 = {D} which contains only the point D, run the K-means clustering algorithm and report the final clusters. Use L1 distance as the distance between points which is given by d ((x1, y1), (x2, y2)) = | x1 - x2 | + | y1 - y2 |. Draw the points on a 2-D grid and check if the clusters make sense. You may stop the clustering process if it found that two iterations havethe same clusters, otherwise, at least 4 iterations are required
• Given are the 1-dimensional points A = 2, B = 3, C = 4, D = 9, E = 10, F = 11. Compute complete-linkage hierarchical clustering using d (x, y) = |x - y| as the distance between points. And also draw a dendrogram of it

Please someone solve this with in one hour with step by step solution !