œA quality characteristic of interest for a tea-bag-filling process is

QUESTION

œA quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are under filled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. In this example, the label weight on the package indicates that, on average, there are 3.40 grams of tea in a bag. If the average amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 215 bags a minute). The following table provides the weight in grams of a sample of 50 bags produced in one hour by a single machine
A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are under filled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. In this example, the label weight on the package indicates that, on average, there are 5.5 grams of tea in a bag. If the mean amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 170 bags a minute). The file Teabags, as shown below, contains the weights, in grams, of a sample 50 tea bags produced in one hour by a single machine: 5.65 5.44 5.42 5.40 5.53 5.34 5.54 5.45 5.52 5.41 5.57 5.40 5.53 5.54 5.55 5.62 5.56 5.46 5.44 5.51 5.47 5.40 5.47 5.61 5.53 5.32 5.67 5.29 5.49 5.55 5.77 5.57 5.42 5.58 5.58 5.50 5.32 5.50 5.53 5.58 5.61 5.45 5.44 5.25 5.56 5.63 5.50 5.57 5.67 5.36 a. compute the mean, median, first quartile, and third quartile b. compute the range,¦

tile range, variance, standard deviation, and coefficient of variation. c. Interpret the measures of central tendency and variation within the context of this problem. Why should the company producing the tea bags be concerned about the central tendency and variation? d. construct a boxplot. Are the data skewed? If so, how? (a) Mean= 5.5014 Median = 5.515 1st quartile =5.440 Third Quartile = 5.570 (b) Range(5.25,5.77) = 5.77 “ 5.25 = 0.52 interquartile range = 5.57-5.44 =0.13 Varince =0.01120004 Standard Deviation =0.1058302 Coefficient of variation =1.923697 (c) Central tendency = 5.5014 and Variation =0.01120004 In order to optimize production and profit need toconcerned about the central tendency and variation (d) (e) P(X<5.5) = P(z<5.5--5.50140/.01120004) =0.99999 Hence, we can say that company is meeting the rquiremen.   ANSWER: CLICK REQUEST FOR  AN EXPERT SOLUTION