A coating that weighs at least 3 mg is needed to impart adequate shelf life to pharmaceutical tablet. Random sampling of 250 tablets revealed that 14 failed to meet this requirement. a) use this info to estimate the relative standard deviation for the measurement. b, what is the 95% confidence interval for the number of unsatisfactory tablets, c, assuming that the fraction of rejects remains unchanged, how many tablets should be taken to ensure a relative standard deviation of 5% in the measurement

Question

A coating that weighs at least 3 mg is needed to impart adequate shelf life to pharmaceutical tablet. Random sampling of 250 tablets revealed that 14 failed to meet this requirement.  a) use this info to estimate the relative standard deviation for the measurement. b, what is the 95% confidence interval for the number of unsatisfactory tablets, c, assuming that the fraction of rejects remains unchanged, how many tablets should be taken to ensure a relative standard deviation of 5% in the measurement

kropot72 · Answer

A binomial distribution is appropriate for this question, where p is the probability of failure and q = 1 - p is the probability of compliance.
p = 14/250 = 7/125
q = 1 - 7/125
The number of samples is n = 250.
The standard deviation is given by:
$$\large SD=\sqrt{npq}=\sqrt{250\times\frac{7}{125}\times(1-\frac{7}{125})}=you\ can\ calculate$$

anonymous · Answer

okay, it is 3.64

kropot72 · Answer

Your result is correct to two decimal places.