a concentration of SO4 in a compound is known to follow uniform distribution. A
ID: 3021785 • Letter: A
Question
a concentration of SO4 in a compound is known to follow uniform distribution. A sample of 44 packs of the compound was taken and the mean of SO4 across these was equal to 1259 ppm, standard deviation was 339ppm.
a) construct a 95% confidence interval for the true mean concentration in ppm of SO4 in the compound. interpret this interval clearly
b)how would answer in part A change if distribution of SO4 concentration was normal apposed to uniform?
c) if you were interessted in ensuring a confidence coefficient of .99 that the interval is within +- 100 ppm and the mean. what sample size would be required?
d) if sample of 100 packs of compound showed that 65 of them had concentrations within acceptable limits, form 95% confidence interval for the true portion of the packs that have acceptable SO4 levels.
Explanation / Answer
a)
confidence interval = mean + / - z-score * std/sqrt(n)
= 1259 +/- 1.645 * 339 /sqrt(44)
= 1259 +/- 84.07
c)
standard error of mean = 100
=>
2.575 * 339/sqrt(n) = 100
=> n = 76.20 = 76
d)
standard error of mean = 1.645 * sqrt(0.65 * 0.35/100) = 0.0785
confidence interval = 0.65 +/- 0.0785
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