Question: The new Twinkle bulb has a standard deviation \(\sigma =35\) hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be \(\bar{X}=\) 500 hours.

(a) Find the margin of error E for a 95% confidence interval. (5 points)

Round your answer to the nearest hundredths.

(b) Construct a 95% confidence interval for the mean life, ? of all Twinkle bulbs. (5 points)