Question: The lifetime (X) of electric light bulbs made by Philips are known to have a mean lifetime of 1120 hours with variance of 427.25. If a sample of 500 bulbs are chosen and their lifetimes observed, what is the probability that the mean lifetime is

\(\begin{aligned} & (a)\,\,\,1117.4<\bar{x}<1124.5? \\ & (b)\,\,\bar{x}>1116.55 \\ & (c)\,\bar{x}<1123.91 \\ & (d)\,\bar{x}>1115.54? \\ \end{aligned}\)