Question

You are required to construct 90% confidence interval for mean life time of tyres from a sample of 250 tyres whose mean is found to be 35,290kms. The population standard deviation is 1024 kms.

Answer 1

$n = 250$

$\bar x = 35290$

$\sigma =1024$

The 90% confidence interval for mean is given by:

$\bar x\pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt n}=\bar x\pm Z_{0.05}\frac{\sigma}{\sqrt n}=35290\pm1.64\cdot\frac{1024}{\sqrt{250}}=35290\pm106$

So the 90% confidence interval estimate for the mean life time of tyres is (35184, 35396)