Question: The scores of applicants to a job in an aptitude test (X) used for the interview are known to be normally distributed with a mean of 50 and variance of 331.24. If a sample of 110 of the applicants is chosen, what is the probability that from the sample, the estimated mean

\(\begin{aligned} & (a)\,\,\,44.89<\bar{x}<55.34? \\ & (b)\,\,\bar{x}>53.45 \\ & (c)\,\bar{x}<46.81 \\ & (d)\,\bar{x}>45.54? \\ \end{aligned}\)