Question

A random sample of 105 light bulbs had a mean life of 441 hours with a standard deviation of 40 hours. Construct a 90% confidence interval for the mean life, mu, of all light bulbs of this type.

Answer 1

The CIE is (434.58 , 447.42)

Answer 2

A z-score of ~1.645 will give a two-tailed confidence level of ~0.9 = 90%.
\[z = \frac{x - \mu}{\sigma}\]
\[z*\sigma = |x - \mu|\]
Where z is the z-score, sigma is the standard deviation, \mu is the mean, and x is the picked score. Solve for both values of x.

Answer 3

Just notices that the standard deviation is that of the sample and not the whole population, therefore this must be done with a T-value instead of a Z-value... so my answer above is incorrect. The 90% CIE should actually be (434.52 , 447.48)