A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. A) What is the probability that the second pipe (with length Y) is more than 0.22 feet longer than the first pipe (with length X)?

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.

In tests of stopping distances for automobiles, those automobiles traveling at 30 miles per hour before the brakes are applied tend to travel distances that appear to be uniformly distributed between two points a and b. Suppose three automobiles are used in a test. Find the probability that exactly one of the three travels past the midpoint between a and b.

TF.13 The English proficiency test scores of the students from a large high school have mean μ = 76 points and standard deviation σ = 8.8 points. Let x̄ be the average salary of a random sample of 40 students. a) Find the probability that x̄ is between 72 and 80, inclusive. b) Find the probability that x̄ is at least 77.