Question

The mean and the standard deviation of the breaking strength of 100 cables tested by the company is 180 lbs and 25 lbs . Find 95% confidence limit of breaking strength of all cables manufactured by the company

Ans: (180- 24.9 , 180+24.9)

Answer 1

95%confidence interval =$\bar x±z_{\alpha/2}\frac{s} {\sqrt n}$

The z score corresponding to 95% confidence interval is 1.96.

$=180±1.96×\frac{25}{\sqrt {100}}$

$=180±4.9$

=(175. 1, 184.9)

We are 95% confident that the limit of breaking strength of all cables manufactured by the company is betwee 175.1 and 184.9.