The yield of a synthetic polymer SSS, measured in milligrams, is modeled by a continuous uniform distribution on the interval [c−10,c+20][c - 10, c + 20][c−10,c+20], where c c\,c is a controlled reaction constant. A large random sample of n n\,n yields is taken during a production run.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean Sˉ\bar{S}Sˉ. Give the parameters of the distribution in terms of n n\,n and c c\,c where appropriate.
The sample mean of the n n\,n observations is recorded as 152.4. Given that the upper bound of a 95% confidence interval for the constant ccc, based on this sample, is 147.89,
calculate the value of nnn. Show your working clearly.
