Answer to Question #187004 in Statistics and Probability for Aparna

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.