Question

I ONLY NEED PART D to be answered . The rest is solved already, I just forgot to add part D on the last

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 96 hours. A random sample of 64 light bulbs indicated a sample mean life of 300 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.

b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 560 hours? Explain.

c. Must you assume that the population light bulb life is normally distributed? Explain.

d.Suppose the standard deviation changes to 80 hours. What are your answers in (a) and (b)?

The 99%confidence interval estimate would be from a lower limit of ___hours to an upper limit of ___hours.

Answer 1

Since the Standard deviation has now been changed to 80. So Your required answer is Lower Limit:

\(276.737\) and Upper Limit: \(323.263\)

Confidence Interval \(=\mu \pm z * \frac{s}{\sqrt{n}}=300 \pm 2.33 \frac{80}{\sqrt{64}}\)

Con fidence Interval \(=300 \pm 23.263\)

Con fidence Interval \(=(276.737,323.263)\)