The article "Monte Carlo Simulation Tool for Better Understanding of LRFD" suggests that yield strength (ksi) for A36 grade steel is normally distributed with = 43 and o = 4.5. (a) What is the probability that yield strength is at most 40? Greater than 60? (b) What yield strength value separates the strongest 75% from the others?

An elephant eats an average of 3 bushels of alfalfa per day, with a standarddeviation of 0.8 bushels. Suppose that you need to feed 10 elephants for oneweek. If the distribution is normal, what is the minimum number of bushels ofalfalfa so that there is no more than a 10% chance of running out by the end of the week?

You believe that your morning commute to UCLA is decreasing every week. You record thetime of 7 commutes (one for each day of the week) (in minutes) for the a one-week block and thenthe following one-week block. * Calculations have been done for you: the sample mean difference is -1.714 and the sample standarddeviation is 2.984. Conduct a hypothesis test at the α = 0.15 level. The mean difference calculated as the the first one-week block minus the second one-week block. That is to say week one minus week two. a. Set up the null and alternative hypothesis (using mathematical notation/numbers and interpretthem in context of the problem) b. Calculate the test statistic for the test from part a

(b) A company has 16 cars of this model in its fleet. What is the probability that the average NOX + NMOG level x¯ of these cars is above 90 mg/mi?   - life for one car model vary Normally with mean 84 mg/mi and standard deviation 6 mg/mi