A pharmaceutical company has developed a new pill that will mitigate the pain suffered during a migraine headache and needs to estimate the mean time it takes for the pill to begin mitigating a migraine headache. A simple random sample of migraine sufferers will be drawn from a large pool of volunteers for this study. If it is known that the minimum time it will take for the pill to begin having an effect is 5 min and the maximum time is 85 min, determine

(a) an estimate of the standard deviation ????.

(b) the sample size required for estimating the mean time with a bound on the error of estimation of 2 min.

(c) cost of sampling when the initial cost is $500 and the cost per sampled unit is

$25.