1 If there are 80 students in a class with an average height of 166 cm and a standard deviation of 4 cm, and the students are randomly split into 16 groups, each with 5 people, what is the standard deviation of the average height among the groups?

a. 1.25

b. 0.8

c. 2.236

d. 1.789

2. A coffee shop claims to have high-quality control over coffee temperatures, and its customers require temperatures to be within a range of 178 to 182 degrees Fahrenheit, what is the standard deviation of the process if the shop has a process capability ratio Cp = 1.67?

a. 0.2

b. 0.6

c. 0.4

d. 0.3

3. Tom has forecasted the number of patients visiting a clinic over the past five days, with his forecasts being 17, 20, 19, 15, and 23. The actual numbers of patients on those days are 16, 18, 24, 21, and 18, respectively. What is the average error of Tom's forecasts? a. -0.6

b. 3.8

c. -3

d. 1

4. Scott is using double exponential smoothing to forecast demand with a trend, and the smoothing factors are = 0.8 and = 0.6 for forecasting the value and trend, respectively. His forecasted demand today is 100, and the forecasted trend for today is 3. The actual demand for today is 98. What is Scott's forecasted trend for tomorrow?

a. 2.48

b. 2.04

c. 1.76

d. 1.4

5.The factory monitors the number of products discarded before completion during the manufacturing process. Each day, it take 200 samples. Over the past four days, it discarded 11, 6, 7, and 12 products, respectively (with a total of n = 800 samples). If the factory uses a p-chart with 3-sigma limits for process control, what is the lower control limit for this p-chart?

a. 0.027

b. 0.023

c. 0.037

d. 0.031

Please answer completely. Thank You !