The quality control manager at a light bulb factory needs to estimate the mean l

Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 104 hours. A random sample of 64 light bulbs indicated a sample mean life of 320 hours. Complete parts (a) through (d) below. a. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment. The 99% confidence interval estimate is from a lower limit of hours to an upper limit of hours (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 370 hours? Explain. Based on the sample data, the manufacturer V the right to state that the lightbulbs have a mean life of 370 hours. A mean of 370 hours is standard erosthe sample mean, so i a V the sample mean, so it is Vthat the lightbulbs have a mean life of 370 hours c. Must you assume that the population light bulb life is normally distributed? Explain

Explanation / Answer

#Chegg policy states to answer only one question when multiple are posted

a) Std dev = 104, sample mean = 320 hours,

SE of mean = std dev/sqrt(n) = 104/sqrt(64) = 104 /8 = 13

CI = sample mean +- z-score (99%) * SE of mean

CI = 320 +- 2.576*13

CI = (286.5, 353.5)

b) The manufacturer does not have the right to say , as the mean 370 is way beyond our 99% confidence interval of 286.5-353.5

c) A) as n = 64 > 30 we can assume normal distribution according to central limit theorem

d) If std dev = 76

CI = 320 +- 76/8 = (310.5, 329.5)

The answer will remain the same and the manufacturer is not right to state the mean life of the bulbs as 370 hours

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