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.

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

Round your answer to the nearest hundredths. . (References: definition of margin of error on page 312 and example 2 on page 312).

(b) Construct a 95% confidence interval for the mean life,  of all Twinkle bulbs. (5 points) (References: example 5 page 315, end of section exercises 51 - 56 pages 319 - 320)

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