1. a) Give the name of the distribution of X M(t)=(0.3+0.7e')' .2 b) Find the value of A and Oʻ c) Calculate P(1

Please don't provide hand written solution

can you solve this for me by showing step by step for each question? Acme Food manufactures and sells bags of doughnuts whose weights follow a normal distribution with a mean of 400g and standard deviation 8g. a) Find the probability that a bag of doughnuts weights less than 410g  b) Find  P (X>412) c) Find P (395 < X < 404) d) The company can be prosecuted if the bags are less than 380g, if the company sells 50 bags per day find the expected number of bags under this weight.  e) On a typical day 1.22% of bags are rejected as they are too heavy. Find the rejection weight.

The lifetime of a certain battery is modeled with the Weibull distribution with α = 2 and β = 0.1. a) What proportion of batteries will last longer than 10 hours? b) What proportion of batteries will last less than 5 hours? c) What proportion of batteries will last longer than 20 hours? d) The hazard function is defined in Exercise 8. What is the hazard at t = 10 hours?