Math 119 Homework Ch 4 Name Read the following examples and identify the key par
ID: 3333072 • Letter: M
Question
Math 119 Homework Ch 4 Name Read the following examples and identify the key parameters of the Binomial Random Variable (n and p) a. 1) In a recent Gallup study, 2,000 randomly selected American adults were interviewed, 54% of those interviewed said they feel better about the economy in recent months. Asuccess is defined as a person saying they feelbetter about the economy What does the Binomial Random Variable X represent in this example? (see slides 12-14 in the Powerpoint notes) ii. Be sure to use words from the example in defining x. b. Another recent Gallup study of 4,500 American adults in September 2015 shows that 60% of American adults say a third major political party is needed because the Republican and Democratic parties "do such a poor job" of representing the American people. Gallup defines "success" as a person agreeing that a third major political party is needed. ii. What does the Binomial Random Variable X represent in this example? The maker of Cracker Jacks (caramel popcorn and peanuts snack) says that 99.8% of their boxes contains a prize (so 0.2% of the boxes are missing the prize by accident). Your buy 25 randomly selected boxes of Cracker Jacks from a variety of stores and look inside each box to see if there is a prize. Success "find a prize in a box" C. n= (fill in the specific values in this example) ii. What does the Binomial Random Variable X represent in this example? ii. How is "failure" defined in this case? (Think of what a failure would look like when opening an individual box) iv. What is the probability that you find a prize in each of the 25 boxes? Does this probability surprise you? 2) Suppose the probability that a college senior will graduate at UCSD is 0.91 (91%). Five college seniors with the same major who have been in a study group together for four years are observed until they graduate (or leave without graduating). X the number of these seniors who graduate i. Define "success" in this example (what would success look like in a single trial?): Il. Why might the sample chosen, five students with the same major who are in the same study group, not be the best "random sample" of college seniors at UCSD?Explanation / Answer
a .
(i)
n is sample size
p is the probability of success
n = 2000, p = 0.54
(ii)
X represent number of American adults who feel better about the economy.
b .
(i)
n is sample size
p is the probability of success
n = 4500, p = 0.60
(ii)
X represent number of American adults who agree that a third major political party is needed.
c.
(i)
n is sample size
p is the probability of success
n = 25, p = 0.998
(ii)
X represent number of boxes containing the prize.
(iii)
A failure is defined as box does not contain the prize.
(iv)
Probability that each of the 25 boxes contains the prize = (0.998)25 = 0.9512
No, finding prize in each box will multiply the probability of single trial 25 times and hence decrease the probability. So, this probability will be less than the probability of single trial.