(iii) Given that the events A and B are such that : 3 P(A) = P(AUB)= and P (B) = p. 2' Find the value of 'p' if the events are independent.

The spinner is spun one time. Find the probabilities. P(A) = P(C) = %3D A A E P(BUC)= P(B©) = Sample Space: P(B U A)= P(B U A)C = %3D P(D^)= P(AN C)= Page B.

2) The number x of people admitted to an intensive care unit in a particular hospital, on any given day, has a Poisson probability distribution with mean equal to five (5) people per day. What is the probability that the number of people admitted to an intensive care unit on a particular day is three (3)? Solve using Poisson's formula (Mendenhall et al., 2015).

Consider three independent events, A1,A2,A3, and let Pi = P(Ai) for i = 1,2,3. Express the probability that at least one of these events occurs in terms of the pi’s

What is the z-score of x = 3 if X ~ N(5,2)? -5 1

Approximately 8% of students at a local high school participate in after-schoold sports every year of hs. A group of 60 seniors is randomly choosen. Of interest is the number who participated in after school aports every year of hs. In words define the variable X, list the values that x may take on, Write the distribution of X mathmatically with correct notation, how many seniors in this group are expected to have participated in after school sports every year of hs, Find the probability that no seniors participated in after school sports every year of hs- list the Excel command used, Based on numerical values would you be suprised if none of the seniors participated in after school sports every year of hs and why?

Suppose that 70% of all students in a large university pass all their classes. Find the probability that more than 60% of 34 r/s students from this university pass all their classes.

Five brothers and their wives decide to have children until each family has two female children. (a) What is the pmf of X = the total number of male children born to the brothers? (Enter combinations using the formula (n choose r).)  (b) What is E(X)? (c) How does it compare to the expected number of male children born to each brother?

Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.

The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem  to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.