Homer performs three simulation studies. His

population is skewed to the right. For one study

he has his computer generate 10,000 random

samples of size n = 10 from the population.

For each random sample, the computer calculates the Gosset 95% confidence interval for

and checks to see whether the interval is correct. His second study is like his first, but

n = 100. Finally, his third study is like the first,

but n = 200. In one of his studies, Homer obtains 9,504 correct intervals; in another he obtains 9,478 correct intervals; and in the remaining study he obtains 8,688 correct intervals.

Based on what we learned in class, match each

sample size to its number of correct intervals.

Explain your answer.

40. Independent random samples are selected from

two populations. Below are the sorted data from

the first population.

362 373 399 428 476 481

545 564 585 589 590 600

671 694 723 724 904

Hint: The mean and standard deviation of these

numbers are 571.1 and 144.7.

Below are the sorted data from the second population.

387 530 544 547 646 766

786 864

Hint: The mean and standard deviation of these

numbers are 633.8 and 160.8.

(a) Calculate Gosset's 90% confidence interval for the mean of the first population

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].

Question 10 Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. X 6 13 19 20 P(X) 0.58 0.1 0.1 0.12 0.1 What is the expected value of X? Submit QuestionPr Feedback Question 12 of 16 Atter Select the true statement(s) about the mean, variance, and standard deviation for a discrete random variable. The variance of a discrete random variable can be negative. The mean of a discrete random variable must be a possible value of the random variable. For any discrete random variable X, the probability that X is within 2 standard deviations of the mean is approximately 0.68. The computational formula for the variance o should be used only when the number of possible values for the random variable is small. The standard deviation of a discrete random variable is always non-negative. v The expected value of a discrete random variable can be negative. Incorrect MacBook Pro3.2.42 Question Help By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A) = = P(A and B) P(A) Use the information below to find the probability that a flight arrives on time given that it departed on time. The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.87. The probability that a flight departs and arrives on time is 0.82. The probability that a flight arrives on time given that it departed on time is(] (Round to the nearest thousandth as needed.) Enter your answer in the answer box and then click Check Answer. All main chewing javascript:doExercise(20); Clear All Check AnswerD Question 15 2.5 pts What is the mean and standard deviation of the discrete random variable called X_Var shown below? X_Var | Prob 3.899 | 0.2898 6,315 | 0.2066 8,060 | 0.1722 8,168 | 0.1750 9,397 | 0.1564 mean = 7,167.80 standard deviation = 3,635,614.96 mean = 6.721.63 standard deviation - 2,033.98 mean = 7.167.80 standard deviation = 2.131.79 mean = 7,167.80 standard deviation = 4,544,518.70 mean = 6,721.63 standard deviation = 4,137,064.56 O mean = 7,167.80 standard deviation = 1,906.73