Question

A random sampling of a company's monthly operating expenses for n=36 months produced a sample mean of $5474 and a stan-dard deviation of S 764. Find a 90% upper confidence bound for the company's mean monthly expenses.

Answer 1

Answer with explanation:

Mean of the sample(m) = $ 5474

Standard deviation of the sample (S)=764

Number of observation(n)=36

$Z_{90 \text{Percent}}=Z_{0.09}=0.5359$

$z_{score}=\frac{\Bar x-\mu}{\frac{S}{\sqrt{n}}}\\\\0.5359=\frac{5474- \mu}{\frac{764}{\sqrt{36}}}\\\\0.5359=\frac{5474- \mu}{\frac{764}{6}}\\\\764 \times 0.5359=6 \times (5474- \mu)\\\\409.4276=32844-6 \mu\\\\6 \mu=32844 -409.4276\\\\ 6 \mu=32434.5724\\\\ \mu=\frac{32434.5724}{6}\\\\ \mu=5405.76$

So, Mean Monthly Expenses of Population =$ 5405.76, which is 90% upper confidence bound for the company's mean monthly expenses.