Problem 2. Jane is going on a date. The time she needs to get ready has the normal distribution with the mean 55 minutes and the standard deviation 5 minutes. (a) Draw the probability density function of Jane's preparation time. Shade on the plot the probability that Jane will need more than 1 hour to prepare for the date. Find this proba- bility by reducing it to the standard normal distribution. (b) Suppose that it is 16:00 now and Jane starts to prepare. Shade on the plot the probability that Jane will be ready in the interval 16:4517 :00. Find this probability by reducing it to the standard normal distribution. Problem 3. One hundred meters is the shortest outdoor sprint race distance. The current men's world record of 9.58 seconds was set in 2009 by Usain Bolt, who nished his sports career. Let's nd the probability that his record will be beaten soon. (a) The winner of 2020 Olympic Games was Lamont Marcell Jacobs, who ran 100m in 9.80 seconds. Suppose that the distribution of his time is normal with the average 10.03 seconds and the standard deviation 0.15 seconds. Find the probability that he can beat the record of Usain Bolt next time he runs in a competition. (b) By how much should Jacobs improve his average time (with the same standard deviation) to be sure to beat Usain Bolt's record with probability 5% in a single run? (0) Answer the same question as in (b), but for the probability to beat the record in a series of 10 runs