Question

A fertilizer mixing machine is set to give 12kg of nitrate for every 100kg bag of fertilizer. A sample of ten such bags is examined. The percentage of nitrates are as follows: 11,14,13,12,13,12,13,14,11,12.
a. calculate the sample mean
b. calculate the sample standard deviations

Answer 1

Answer:

Missing point in question :-  Is there any reason to believe that the machine is

defective?

Answer:-

If the probability of bags ≠ 12 kg is >  5% , then there is every reason to believe that the machine is  defective.

Out of 10 samples:-  11, 14, 13, 12, 13, 12, 13, 14, 11, 12​ only 3 , 12 kg bags are seen in sample. So probability of  bags ≠ 12 kg =  70%

Now, the sample size was only 10 bags out of 100. So the probability when extended to 100 bags become = 1/10 x 70% = 7%

Since 7%  >  5% , then there is every reason to believe that the machine is  defective