## anonymous 5 years ago 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.

1. anonymous

The CIE is (434.58 , 447.42)

2. anonymous

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.

3. anonymous

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)