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?)

36. Consider all courtroom trials with a single defendant who is charged with a felony. Suppose

that you are given the following probabilities for

this situation.

Seventy-five percent of the defendants are, in

fact, guilty. Given that the defendant is guilty,

there is a 70 percent chance the jury will convict the person. Given that the defendant is not

guilty, there is a 40 percent chance the jury will

convict the person.

For simplicity, assume that the only options

available to the jury are: to convict or to release

the defendant.

(a) What proportion of the defendants will be

convicted by the jury?

(b) Given that a defendant is convicted, what

is the probability the person is, in fact,

guilty?

(c) What is the probability that the jury will

make a correct decision?

(d) Given that the jury makes an incorrect decision, what is the probability that the decision is to release a guilty person?

37. Recall that a confidence interval is too small if

the number being estimated is larger than every

number in the confidence interval. Similarly, a

confidence interval is too large if the number

being estimated is smaller than every number

in the confidence interval.

Each of four researchers selects a random sample from the same population. Each researcher

calculates a confidence interval for the median

of the population. The intervals are below.

[24, 41], [30, 39], [20, 33], and [35, 45].

3. Drake Marketing and Promotions has randomly surveyed 200 men who watch professional sports. The men we're separated according to their educational level (college degree or not) and whether they preferred the NBA or the NFL. The results are shown below: College Degree No College Degree Totals Prefer NBA 40 55 95 Prefer NFL 10 95 105 Totals 156 200 It might help to start by making a new column and row for totals. (a) What is the probability that a randomly selected survey participant prefers the NEL? 105 200 (b] What is the probability that a randomly selected survey participant has a college degree and prefers the NBA?. 95 (c) Suppose a survey participant is randomly selected and you are told that he has a college degree. What is the conditional probability that this man prefers the NFL? (d) Are the two events, "College degree" and "Prefer NFL" independent? (Justify your answer] 4. Find the following probabilities using multiplication rules and conditional probability definitions. (a) Suppose that E and F are two events and that P(E and F) = _6 and P(E) = .8. What is P(FIE]? (b) Suppose that E and F are two events and that P(E) = 6 and P(FE) = .4. What is P(E and F]? (c] Suppose that E and F are two events and that P[E and F) = .4 and P(FIE) = .6. What Is P(E]?IQuestion Help A modified box-and-whisker plot is a box-and whisker plot that uses symbols to identify outliers. The horizontal line of a modified box-and-whisker plot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. (a) Identity any outliers and (b) draw a modified box-and-whisker plot that represents the data set. 10 15 25 8 10 15 2 13 13 13 10 10 10 11 (a] Identify arry outliers. Select the correct choice below and. If necessary, fill in the answer box to complete your choice. O A. The outlions) is(are) (Type an integer of decimal. Use a comma to separate answers as needed.) O B. There are no outliers. (b) Choose the correct modified box-and-whisker plot below. OA. 10 20 30 10 20 19 20 30myopenmath.com C nMath Home | My Classes . | Help | Log Out orums Calendar Gradebook g 2019 > Assessment The Multiplication Rule and Conditional Probability A large cooler contains the following drinks: 10 lemonades, 5 Sprites, 14 Cokes, and 12 root beers. You two cans, one at a time (without replacement). Compute the following probabilities. (a) What is the probability that you get two cans of Sprite? Preview (b) What is the probability that you do not get two cans of Coke? Preview (c) What is the probability that you get either two root beers or two lemonades? Preview (d) What is the probability that you get one can of Coke and one can of Sprite? Preview (e) What is the probability that you get two drinks of the same type? Preview Get help: Video Video Points possible: 1 Unlimited attempts. Score on last attempt: (0.2, 0, 0.2, 0, 0.2), Score in gradebook: (0.2, 0, 0.2, 0, 0.2), Out of: (0.2, 0.2, 0.2, 0.2, 0.2) 12 DI FS #7Section 4.3: The Multiplication Rules and Conditional Probability. Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such way that the probability is changed, the events are said to be dependent events. Example # 19: Determine whether these events are dependent or independent a) Tossing a coin and drawing a card from a deck. b) Drawing a ball from an urn, not replacing it, and then drawing a second ball. c) Drawing a ball from an urn, replacing it, and then drawing a second ball. Multiplication Rule 1 When two events A and B are independent, the probability of both occurring is P(A and B) = P(A)-P(B) Example # 20: A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die. Example # 21: An urn contains 5 red balls and 3 white balls. A ball is selected and its color noted. Then it is replaced. A second ball is selected and its color noted. Find the probability of each of these. a) Selecting two red balls. b) Selecting two white balls. c) Selecting I red ball and then I white ball. 11