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)

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)(\sigma)/(√(n))`

`=75\pm(2.576)*(10)/(√(50))\\\\\approx75\pm3.64\\\\=(71.36,\ 78.64)`

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