Question: The new Twinkle bulb has a mean life of hours with a standard deviation \[\sigma =35\] hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be \[\overline{X}=\] 550 hours.

a. Find the margin of error E for a 90% confidence interval. (5 points)

Round your answer to the nearest hundredths.

b. Construct a 90% confidence interval for the mean life, m of all Twinkle bulbs. (5 points) (References: example 5 page 315, end of section exercises 51 - 56 pages 319 - 320)