please help me with the following problems:

A book shelf manufacturer claims that their largest bookshelves can withstand an average of 250 kilograms of books, with a standard deviation of about 22 kilograms. A sample of 46 bookshelves is selected and the weight they could withstand was measured. Using this Information, answer the following questions. For full marks your answer should be accurate to at least three decimal places. a) What is the probability that the value of the sample mean is less than 246.9 or greater than 253.1? Probability: 0 b) What is the probability that the value of the sample mean is less than 243.9? Probability: 0Suppose X is a random variable whose distribution has mean 19.1 and standard deviation 14. If we draw random samples of size 40 from the population and take the mean of the sample values, these yield a new random variable X. For full marks your answer should be accurate to at least two decimal places. a) Find the expected value of X. HX = 0 b) Find the standard deviation X. OX = 0LifeCharge Batteries claims that their batteries last an average of 255 hours when used in a hand held gaming system, with a standard deviation of about 14 hours. An independent quality control company took a sample of 41 batteries, and used the same hand held gaming system that LifeCharge used to record the time the batteries lasted. Using this information, answer the following questions. For full marks your answer should be accurate to at least three decimal places. a) What the probability that the value of the sample mean is less than 254.2 hours? Probability: 0