14. A machine can be adjusted so that when under control, the mean amount of powdered soap filled in a bag is 5 kilos. From past experience, the standard deviation of the amount filled is known to be...

14. A machine can be adjusted so that when under control, the mean amount of powdered soap filled in a bag is 5 kilos. From past experience, the standard deviation of the amount filled is known to be 0.15 kilos. To check if the machine is under control, a random sample

of sixteen bags was weighed and the mean weight was found to be 5.1 kilos. At 1% significance level, is the adjustment our of control? (Assume a normal distribution of the amount of powered soap filled in a bag.)

15. A paint manufacturing company claims that the mean drying time for its paints is 45minutes. A random sample of 35 gallons of paints selected from the production line of this company showed that the mean drying time for this sample is 50 minutes with a standard deviation of 3 minutes. Assume that the drying time for these paints have a normal distribution. Using 1% significance level, would you conclude that the company’s claim is true?