7. Recall the password manager question, which was Question 6 on Home- work 4. There were 82 yesses and 87 noes. (a) If all 169 people use a password manager, what would the distribution of the number of yesses be? Include any parameters. (b) If none of the 169 people use a password manager, what would the distribution of the number of yesses be? Include any parameters. (c) Suppose we would like to believe that all 169 people use a password manager. Let us make that our null hypothesis, which we will believe unless the data does not support it. We will reject the null hypothesis if there are too few yesses. Approximate the probability that there are 82 or fewer yesses assuming everyone uses a password manager. (d) Based on the probability of seeing 82 or fewer yesses assuming everyone uses a password manager, would you reject the null hypothesis or not? (e) Suppose we have two people answer that homework question. One of them uses a password manager and the other does not. What is the p.m.f. of the number of yesses between those 2 people? (f) Does the number of yesses from those 2 people have a binomial distri- bution? If yes, give the parameters. If no, please explain