Statistics problems

1. The zoo is conducting an annual review of its new apiary. A sample of 50 bees were weight and the average weight of the sample was 4 ounces (yes these are big bees). What is the 99% confidence interval on the average? The known standard deviation is .05 ounces.

2. What is the probability of having 2 consecutive points above the upper control limit on a Standard X-bar R chart, (with 3 control limits) assuming that the points are independent?

3. A study was conducted on microwave ovens. At the end of the shift the operator found 45 defects (nonconformities, including scratches, faulty door handles, cracked glass doors) in total on 75 units. What is the expected percent of nonconforming microwave ovens?

55%

30%

45%

60%

4. The Lower and Upper specification limits on an engine block (length) for an car is 120 - 150 inches. 30 samples, each of 5 engine blocks were measured, and the average range across all samples was 10 inches. Assuming that the process is stable use the sample data to evaluate if the process is 6 capable ? If x = 130, calculate C_pk

5. Jenny likes burgers, she frequents smashburger in Tempe and orders a hamburger with Swiss cheese, bacon, tomatoes, onion rings, mushrooms, pickles, lettuce, mayo and mustard on a whole wheat bun. Including the patty, her order consists of 10 components that are assembled sequentially. If each component is independent and has a 95% chance of meeting Jenny's quality standard, what is the probability that Jenny will be a satisfied customer every week if she frequents the restaurant 3 times/week.