Referring to Q3, suppose that the standard deviation of the random deviation 휖is 350 psi. a. What is the probability that the observed value of 28-day strength will exceed Assignment 9Student Name: ID: Section:pg. 25000 psi when the value of accelerated strength is 2000? (5 marks)b. Repeat part (a) with 2500 in place of 2000. (3 marks)c. Consider making two independent observations on 28-day strength, the first for anaccelerated strength of 2000 and the second for x = 2500. What is the probability that thesecond observation will exceed the first by more than 1000 psi? (5 marks)d. Let Y1and Y2denote observations on 28-day strength when x =x1and x =x2, respectively. By how much would x2have to exceed x1in order that P(Y2>Y1) =.95

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.