A company has been running a particular manufacturing process for 3 years and has accumulated a large amount of data on the number of defective items produced each day. Data from 600 days of production gives the number of defective items per day: X - Number of Defective Items Number of Days 0 75 X-Number of Defective Items Probability 1 180 a. Convert the data to a probability distribution b. What is the probability that there are between 2 and 4 defective items inclusive in one day C. What is the expected number of defective items per day d. What is the standard deviation of the number of defective items per day (Check: 1.408) 0 0.15 2 150 1 0.35 3 90 The company has been approached to purchase a new process. The supplier is promoting that the new process will produce fewer defectives on average and has provided the following probability distribution as evidence 2 0.175 4 65 3 ?? 5 40 4 0.1 5 0.1 f. e. Calculate the Expected Value and Standard Deviation of the number of defectives for the new process Does this data support the suppliers claim that the process is better. Use both the expected value and the standard deviation to answer the question. Question 2 90% of all Data Analysis students who complete all of the THA's pass the subject. Unfortunately only 50% of students do all of the THA's. Overall 80% of students pass Data Analysis. What is the probability that a student who did not complete all of the THA's will fail Data Analysis?