Answer to Question #252488 in Statistics and Probability for Ratna

Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally

distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780

hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm

Answer 1

Solution:

The critical value for z distribution for lower tail and at 96% level of significance is 2.05.

The 96% confidence interval for the population mean of all bulbs produced by this firm is obtained below:

$\bar x\pm z_{\alpha/2}(\dfrac{\sigma}{\sqrt n}) \\=780\pm2.05(\dfrac{40}{\sqrt{30}}) \\=780\pm14.97 \\=(765.03,794.97)$