(3 QUESTIONS) STATISTICS AND PROBABILITY

Neil is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he nds that it is 2.23 oz. The manufacturer's website states that the average weight of each stick is 1.85 02 with a standard deviation of 0.18 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.23 oz or greater? Give your answer as a percentage precise to at least two decimal places. You might nd this table of standard normal critical values useful. .25 80 % Incorrect Suppose that a random variable Z has a standard normal distribution. Find a such that P(Z > a) = 0.151. Give your answer to two decimal places. You may nd this Z table useful. Suppose Gabe, an elementary school student, has just nished dinner with his mother, Judy. Eyeing the nearby cookie jar, Gabe asks his mother if he can have a cookie for dessert. She tells Gabe that she needs to check his backpack to make sure that he nished his homework. Gabe cannot remember where he left his backpack, but he knows for sure that he did not complete his homework and will not be allowed to eat a cookie. Gabe believes his only option is to quickly steal a cookie while his mother is out of the room. Judy then leaves the room to look for Gabe's backpack. Assume that Judy could return at any time in the next 90 seconds with equal probability. For the rst 40 seconds, Gabe sheepishly wonders if he will get caught trying to grab a nearby cookie. After waiting and not seeing his mother, Gabe decides that he needs a cookie and begins to take one from the jar. Assuming it takes Gabe 30 seconds to grab a cookie from the jar and devour it without a trace, what is the probability that his mother returns in time to catch Gabe stealing a cookie? Please round your answer to the nearest two decimal places. P(Gabe gets caught) = C]