Since the implementation of an SPC program in the foundry department in January 1990, the engineers had made one change in the foundry operations, which appear to have resulted in a 4% reduction in the scrap rate from the 1989 average rate of 28% (the standard deviation was 2%) The table summarizes the weekly scrap rate data for the first half of 1990. i123456789 10 11 12 13 X 26.4 25.3 31.8 27.1 28.5 20.2 19.3 22.7 20.4 19.5 21.7 24 22.6 (a) Construct a CUSUM chart to analyze the data and verify the engineer's claim regarding the scrap reduction. Please use h = 5 and k = 0.25. and K=ko=0.25*2=0.5, H=ho=5*2=10. A table like this may help with your calculation: i - X₁ X₁(HK) | C† N+ (μo-K) - X₁ Ci NIC or OC? 1 2 13 (b) What is the starting point that an out-of-control sample appears? (c) What is the magnitude of the mean shift?

John Kittle, an independent insurance agent, uses a five-year moving average to forecast the number of claims made in a single year for one of the large insurance companies he sells for. He has just discovered that a clerk in his employ incorrectly entered the number of claims made four years ago as 1,400 when it should have been 1,200.a. What adjustment should Mr. Kittle make in next year’s forecast to take into account the corrected value of the number of claims four years ago?b. Suppose that Mr. Kittle used simple exponential smoothing with a = .2instead of moving averages to determine his forecast. What adjustment is now required in next year’s forecast? (Note that you do not need to know the value of the forecast for next year in order to solve this problem.)

analyze This figure plots the changes in Vietnam’s TB during the period January 2010 – December 2019

2. In 1990, there were 3,300 births in LaPorte County. In 2010, there were 4,200 births in that same county. (a) 2010. Round to the nearest whole number. Use the data above to compute the average rate of change in population from 1990 to Interpret the average rate of change found in part a in a complete sentence.