help please

AlmostReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your class questions this claim. Together as a class, you randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly, what is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 16.7 hours or less? Is the company's claim reasonable?

a) find the random variable and state what does it denote

b) what distribution does the random variable follow and why? justify choice of distribution

c) list the parameters and their values of this distribution

d) write the distribution in mathematical terms and list all the possible values the RV can take on

e) list if the question is or is not about sampling distribution. if answer is about sampling distribution, list the corresponding sampling distributions and explain why

f) to find the probability by R, what is used? what is the result an