Question

The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded X¯¯¯ = 75 lb, and we know that σ2 = 100 lb. Calculate a 99 percent confidence interval for μ.

Answer 1

Answer: (71.36, 78.64)

Step-by-step explanation:

Given : Sample size : n= 50

Sample mean : $\overlien{x}=75\text{ lb}$

Variance : $\sigma^2=100\text{ lb}$

Standard deviation : $\sigma=10\text{ lb}$

Significance level : $1-0.99=0.01$

Critical value : $z_{\alpha/2}=\pm2.576$

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$=75\pm(2.576)\times\dfrac{10}{\sqrt{50}}\\\\\approx75\pm3.64\\\\=(71.36,\ 78.64)$

Hence, the 99% confidence interval for population mean $\mu$ = (71.36, 78.64)