Answer to Question #294636 in Statistics and Probability for Yaku

Question

a) The weight (in ounces) of a frozen food package produced by a given

manufacturer is a normal random variable with mean $\mu$ and variance

$\sigma$² (both unknown). We weigh n = 10 of these packages, selected at random and independently from those produced by this manufacturer and find

\sum_{i=1}^10 x_i = 159,

\sum_{i=1}^10 x^2_i = 2531,

i) Estimate the true average weight of all packages produced by this

manufacturer using a 95% confidence interval.

ii) Find a 95% upper limit confidence interval for $\mu$ .

iii) Determine a 95% confidence interval for the true standard deviation, $\sigma$ .