Consider a population of 1024 mutual funds that primarily invest in large companies. You have determined that μ​, the mean​ one-year total percentage return achieved by all the​ funds, is 9.70 and that σ​, the standard​ deviation, is 1.75. Complete​ (a) through​ (c).

a. According to the empirical​ rule, what percentage of these funds is expected to be within ±3 standard deviations of the​ mean?

b. According to the Chebyshev​ rule, what percentage of these funds are expected to be within ±2 standard deviations of the​ mean ​(Round to two decimal places as​ needed.)

c. According to the Chebyshev​ rule, at least 88.89% of these funds are expected to have​ one-year total returns between what two​ amounts? ​(Round to two decimal places as​ needed.)

Suppose we roll a fair dice thrice in such a way that the assumption of random sampling is satisfied. Let {X1;X2;X3} be the numbers coming up in the first three throws.

Let their sample average be X3= (1/3) * ((X1+X2+X3))

1) Write down the sampling distribution ofX3. To this end, you need to write down a table that contains all values that X3 can take on together with their probabilities.

2) What is the probability that X3 greater than equal to 5, given that the dice is fair?

Exercise 31.1. Rope checks. In a certain manufacturing process, an automated quality control computer checks 10 yards of rope at a time. If no defects are detected in that 10-yard section, that portion of the rope is passed on. However, if there is a defect detected, a person will have to check the rope over more carefully to determine where (measured from the left side in yards) the defect is. If exactly 1 defect is detected in a rope section, we would like to find the probabilities for its location.

a. Why is this a Continuous Uniform problem?

b. What does X represent in this scenario?

c. What are the parameters in this scenario?

d. What is the expected value for the location of the defect?

e. What is the standard deviation?

f. What is the probability density function? Write it in function notation.

g. What is the cumulative distribution function? Write it in function notation.

h. Find P(X > 8). i. Find P(2.3 ≤ X ≤ 5.2) j. Find P(X < 2|X < 5)

i. Find the probability that a defect is within 1 standard deviation of the expected value. (Label this k.)

The time necessary to complete a certain assembly-line task varies according to many factors: fatigue or freshness, worker skill, whether the required parts are available promptly, and so forth. Suppose that this variation may be adequately modeled using a normal distribution with mean 15 minutes and standard deviation 2 minutes.  The quickest 10% of the assembly times are to be rewarded. How fast must an assembly be performed in order to be rewarded?  

The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts​ (a) and​ (b) below. Actress left parenthesis years right parenthesisActress (years) 2525 2626 2828 2828 3333 2626 2525 4545 3131 3333 Actor left parenthesis years right parenthesisActor (years) 6161 3434 3737 4141 3131 3737 4848 4242 3737 3838 a. Use the sample data with a 0.010.01 significance level to test the claim that for the population of ages of Best Actresses and Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​ Actors). In this​ example, mu Subscript dμd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ actress's age minus the​ actor's age. What are the null and alternative hypotheses for the hypothesis​ test? Upper H 0H0​: mu Subscript dμd ▼ less than< greater than> equals= not equals≠ nothing ​year(s) Upper H 1H1​: mu Subscript dμd ▼ greater than> equals= not equals≠ less than< nothing ​year(s) ​(Type integers or decimals. Do not​ round.) Identify the test statistic. tequals=nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals=nothing ​(Round to three decimal places as​ needed.) What is the conclusion based on the hypothesis​ test? Since the​ P-value is ▼ greater than less than or equal to the significance​ level, ▼ fail to reject reject the null hypothesis. There ▼ is not is sufficient evidence to support the claim that actresses are generally younger when they won the award than actors. b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)? The confidence interval is nothing ​year(s)less than

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. Brand Price Score Bose 190 78 Scullcandy 160 76 Koss 95 61 Phillips/O'Neill 70 57 Denon 80 40 JVC 45 27 a. Does the t test indicate a significant relationship between price and the overall score? The test t-Conclusion at α = .05 t = (to 2 decimal places.) p-value is What is your conclusion? Use α = .05. . b. Test for a significant relationship using the F test. p-value is What is your conclusion? Use α = .05. Because p-value is .05, we H0: β1 is . c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value

The Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table are obtained for four counties in one region. (Give all answers to four decimal places.)

C. If one Hispanic person is selected at random from this region, what is the estimated probability that the selected individual is from Ventura?

(e) If one person is selected at random from this region, what is the estimated probability that the person is either Asian or from San Luis Obispo County?


(f) If one person is selected at random from this region, what is the estimated probability that the person is Asian or from San Luis Obispo County but not both?


(g) If two people are selected at random from this region, what is the estimated probability that both are Caucasians?


(h) If two people are selected at random from this region, what is the estimated probability that neither is Caucasian?


(i) If two people are selected at random from this region, what is the estimated probability that exactly one is a Caucasian?


(j) If two people are selected at random from this region, what is the estimated probability that both are residents of the same county?


(k) If two people are selected at random from this region, what is the estimated probability that both are from different racial/ethnic groups?

A company manufactures and markets a traditional type of disposable coffee cup that is used in many fast food restaurants. The company has created a new cup that it believes insulates better than the traditional cup. To investigate whether the new cup insulates better, the company plans to conduct a study. In the study, a random sample of cups for each of the two types will be selected. In each sample, each cup will be filled with the same amount of coffee that has been heated to 150 degrees Fahrenheit (ºF). The amount of time (in minutes) it takes for the coffee to cool to 100º F will be measured for each cup.

The hypotheses that the company will test are shown below, where µ_N is the true mean time it takes coffee to cool from 150º F to 100º F in the new cup and µ_T is the true mean time it takes coffee to cool from 150º F to 100º F in the traditional cup.

H₀: μ_N = μ_T

H_a: μ_N > μ_T

1. Describe a Type II error in the context of the study.

2. The company is concerned about the probability of a Type II error. Which test procedure, one that uses a significance level of ? = 0.10 or one that uses a significance level of ? = 0.01, would result in a smaller probability of a Type II error? Explain.

3. The marketing department in the company has suggested that a 2-minute increase in the time it takes the coffee to cool from 150º F to 100º F would be a noticeable improvement to customers. Suppose the company statistician estimates that the power of the appropriate significance test is 0.88 when the true mean cooling time for the new cups is 2 minutes greater than the true mean cooling time for the traditional cups. Interpret the value of 0.88 in the context of the study.

In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a customer a new automobile: the aggressive approach and the passive approach. For 1160 customers, the following record was kept:

Suppose a customer is selected at random from the 1160 participating customers. Let us use the following notation for events: A = aggressive approach, Pa = passive approach, S = sale, N = no sale. So, P(A) is the probability that an aggressive approach was used, and so on.

(a) Compute P(S), P(S | A), and P(S | Pa). (Enter your answers as fractions.)

(b) Are the events S = sale and Pa = passive approach independent? Explain.

Yes. The two events can occur together.

No. P(S) ≠ P(S | Pa).    

Yes. P(S) = P(S | Pa).

No. The two events cannot occur together.

(c) Compute P(A and S) and P(Pa and S). (Enter your answers as fractions.)

(d) Compute P(N) and P(N | A). (Enter your answers as fractions.)

(e) Are the events N = no sale and A aggressive approach independent? Explain.

No. The two events cannot occur together.

Yes. P(N) = P(N | A).    

Yes. The two events can occur together.

No. P(N) ≠ P(N | A).

(f) Compute P(A or S). (Enter your answer as a fraction.)
P(A or S) =

A study of college football games shows that the number of holding penalties assessed has a mean 2.3 of penalties per game and a standard deviation 1.05 of penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.25 penalties per game or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

"Contingency table below; Calculate the Chi^2 value"

Please include Excel functions or calculations if possible.

"Accident" in R package vcdExtra gives a 4-way table of frequencies of traffic accident victims in France in 1958. See: help(Accident, package="vcdExtra")

I want to create a binomial distribution with the response variable "result" (died or injured). In particular, I want to create a one-way frequency table with:

-age and frequency of injured

-mode and frequency of injured

-age and frequency of died

-mode and frequency of died

What is the code for making a one-way frequency table?