Can you please provide a simple, explanation for solving this problem please?

A manufacturer produces light bulbs that have a mean life of 500 hours when the production process is working properly. Based on experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is not equal to 500 hours.Please label each answer section with the corresponding letter.

a. What are the appropriate H0 and H1 for hypothesis testing?

b. Using a level of significance =0.05, what are the rejection and non-rejection regions in the unit of hours if we use the sample mean of 100 randomly selected light bulbs as the test statistic?

c. A sample of 100 light bulbs was selected, and their mean is 485 hours. What is your conclusion on the hypotheses based on part a and part b?

d. What is the p-value associated with the sample mean equal to 485?