A) Access the pop-up window for the binomial distribution by going to Calc, selecting Probability Distributions, and then clicking on the Binomial... option. The option input constant allows you to enter the value of x for which Pr(X=x). Suppose there is a 10% chance that an individual has a certain genetic marker. Determine the probability that in a town of 50,000 individuals, there are at most 5,100 people with the genetic marker. Also, what is the value of x such that Pr(X x)=0.99 ? B) Suppose trees are distributed in a forest according to a Poisson process with an average number of 80 trees per acre. What is the probability of there being at least 90 trees in a given acre of forest? What is the 75% percentile for this distribution? C) Suppose a lightbulb has lifetime modeled by an exponential distribution with the average lifetime equal to 1000 days. What is the chance that the battery lasts for 1500 days? What is the first quartile for the lifetime of the lightbulbs? D) Suppose a random experiment has chance p of success, r=1, 2, 3,... is an integer, and X is the total number of trials before r many successes are counted. We say that Xhas a negative binomial distribution. A pediatrician wishes to recruit 5 couples, each of whom is expecting their first child, to participate in a new natural childbirth regimen. If there is a 20% chance a couple is willing to participate, what is the probability that at most 15 couples must be asked before 5 are found who agree to participate in the new regimen?