21. A random sample of size n = 250 yields 80

successes. Calculate the 95% confidence interval for p.

22. A random sample of size n = 452 yields 113

successes. Calculate the 95% confidence interval for p.

23. George enjoys throwing horse shoes. Last week

he tossed 150 shoes and obtained 36 ringers.

(Ringers are good.) Next week he plans to

throw 250 shoes. Assume that George's tosses

satisfy the assumptions of Bernoulli trials.

(a) Calculate the point prediction of the number of ringers that George will obtain next

week.

(b) Calculate the 90% prediction interval for

the number of ringers George will obtain

next week.

(c) It turns out that next week George obtains

62 ringers. Given this information, comment on your answers in parts (a) and (b)

25. Bert computes a 95% confidence interval for p

and obtains the interval [0.600, 0.700]. Note:

Parts (a) and (b) are not connected: Part (b) can

be answered even if one does not know how to

do part (a).

(a) Bert's boss says, "Give me a 90% confidence interval for p." Calculate the answer

for Bert.

(b) Bert's boss says, "Give me a 95% confidence interval for p?q." Calculate the answer for Bert. (Hint: p?q = p?(1?p) =

2p ? 1. Bert's interval says, in part, that

"p is at least 0.600;" what does this tell us

about 2p ? 1?)

26. Maggie computes a 95% confidence interval for

p and obtains the interval [0.50, 0.75]. Note:

Parts (a) and (b) are not connected: Part (b) can

be answered even if one does not know how to

do part (a).

(a) Maggie's boss says, "Give me a 95% confidence interval for p

2

." Calculate the answer for Maggie. (Hint: The interval says,

in part, that "p is at most 0.75;" what does

this tell us about p

2

?)

(b) Maggie's boss says, "Give me a 95% confidence interval for p ? q." Calculate the

answer for Maggie. (Hint: p ? q = p ?

(1 ? p) = 2p ? 1. The interval says, in

part, that "p is at most 0.75;" what does

this tell us about 2p ? 1?)

\fPart B. For some events C and D, suppose that P(C) = 0.2, P(D) = 0.4, and P(C n D) = 0.1. Can C and D be independent events? O Maybe O Yes O No O Cannot be determined based on the information given Can C and D be disjoint events? O Maybe O No O Cannot be determined based on the information given O Yes Using the definition of the conditional probability, find the following probabilities: P(C | D) = P(D | C) = Part C. For some events E and F, suppose that P(F) = 0.3, P(E | F) = 0.4, and P(E | FC) = 0.2. To find P(E / F), what probability rule/law, should you use? O The law of total probability O Axioms of probability O Definition of the conditional probability O The addition rule O Definition of the independent events O The multiplication rule for P(A / B) O Bayes' theorem Find P(E / F). To find P(E), what probability rule/law, should you use? O Bayes' theorem O Axioms of probability O Definition of the conditional probability O The law of total probability O Definition of the independent events O The multiplication rule for P(A / B) O The addition rule Find P(E).Part A. For two independent events A and B, suppose that P(A) = 0.2 and P(B) = 0.4. To find P(A /7 B), what probability rule/law, should you use? O Axioms of probability O Definition of the independent events O The law of total probability O The multiplication rule for P(A / B) O Definition of the conditional probability O Bayes' theorem O The addition rule Find P(A / B). To find P(A U B), what probability rule/law, should you use? O The multiplication rule for P(A / B) O Definition of the conditional probability O Bayes' theorem O The law of total probability The addition rule O Definition of the independent events O Axioms of probability Find P(A U B).Understand definitions of events, outcomes, trials, independent/dependent events, and mutually exclusive events Use and, or, and not notation to describe events Use conditional probability notation to describe events Compute basic probability in a situation where there are equally-likely outcomes Compute probability involving and, or, and not . Compute probability using the complement rule Understand mutually exclusive events Find the conditional probabilities of independent and mutually exclusive events . Distinguish between independent or mutually exclusive events given conditional probability information . Use the multiplication rule for conditional probabilities Use the multiplication rule for independent event probabilities Use addition rule for probabilities Use addition rule for mutually exclusive event probabilities . Interpret and complete a contingency table . Use a contingency table to find conditional probabilities . Use a tree diagram to list outcomes and compute probabilities . Use a Venn diagram to compute compound and conditional probabilities