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].

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?)

Box & Whisker Plot Worksheet 1 1. The box and whisker plot below shows the volunteer service hours performed by students at Indian Trail Middle School last summer. Volunteer Service Hours 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 a. What is the median of the data set? b. What is the lower quartile of the data set? c. What is the upper quartile of the data set? d. What percentage of data is between the lower quartile and the upper quartile? 2. What is the median of the following box and whisker plot? What percentage of the data is below the median? 25 30 35 40 5011 - Five Number Summary and Boxplots LEARNING OBJECTIVE: Identify the quartiles in a box-and-whisker plot. .OOD A box-and-whisker plot has been constructed for the following data: 6, 8, 11, 12, 15, 18, 23, 29, 35, and is presented below. 15 23 35 10 20 30 According to this box-and-whisker plot, the third quartile (Q3) value is O .) 15 O b.) 11 O .) 35 ( d.) 23What is the five number summary of the following box and whisker plot? 50 60 70 80 90 100 Create a box and whisker plot with the following set of data: 3, 2, 3, 4, 6, 6, 7O 70 80 90 100 The second box-and-whisker plot is shifted to the right and less spread out (10% less). Lower extreme = 81, lower Q = 64,median = 74,upper Q = 85, upper extreme = 94 O 60 70 80 90 The second box-and-whisker plot is shifted to the right and less spread out (10% less). Lower extreme = 64,lower Q = 74,median = 81,upper Q = 85, upper extreme = 94 O 80 90 100 The second box-and-whisker plot is shifted to the right and more spread out (10% more). Lower extreme = 64,lower Q = 74,median = 81,upper Q = 85, upper extreme = 94 O 60 70 90 The second box-and-whisker plot is shifted to the right and less spread out (10% less). Lower extreme = 85,lower Q = 74,median = 81,upper Q = 64,upper extreme = 94 O 70 90 100 The second box-and-whisker plot is shifted to the right and more spread out (10% more)