The Laurenster Corporation needs to set up an assembly line to produce a new product. The fol- lowing table describes the relationships among the activities that need to be completed for this product to be manufactured.

   DAYS    IMMEDIATE

ACTIVITY    a m                     b                      PREDECESSORS

A 3                      6                      6                                  —                              

B                     5                      8                      11                                A                                

C                     5                      6                      10                                A                                            

D                     1                      2                      6                                  B, C                            

E                      7                      11                    15                                D                                

F                      7                      9                      14                                D                                

G                     6                      8                      10                                D                                

H                     3                      4                      8                                  F, G                            

I                       3                      5                      7                                  E, F, H

a) Develop a project network for this problem.

b) Determine the expected duration and variance for each activity.

c) Determine the ES, EF, LS, LF, and slack time for each activity. Also determine the total

    project completion time and the critical path(s).

d) Determine the probability that the project will be completed in 34 days or less.

e) Determine the probability that the project will take longer than 29 days.

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Given f(x,y) = 2 ; 0< x ≤ y < 1

a. Prove that f(x,y) is a joint pdf.

b. Find the correlation coefficient of X and Y.

1.

John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month,

plus a commission. His monthly commission is normally distributed with mean $10,000

and standard deviation $2,000. John's income levels from these two sources are

independent of each other. Use this information to answer the following questions:

a) for a given month, what is the probability that John's commission from the jewelry store is less than $13,000?

b) for a given month, what is the probability that John's commission from the jewelry store is at least $12,000?

c) for a given month, what is the probability that John's commission from the jewelry store is between $11,000 and $12,000?

d) the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month?

e) the probability is 0.75 that John's commission from the jewelry store is less than?

f) how much in a given month?

2) The amount of time a bank teller spends with each customer has a population mean m = 3.10 minutes and standard deviation s = 0.40 minute. If a random sample of 16 customers is selected.

What is the distribution of the mean amount of time for the samples?

What is the probability that the average time spent per customer will be at least 3 minutes?

There is an 85% chance that the sample mean will be below how many minutes?

If a random sample of 64 customers is selected, there is an 85% chance that the sample mean will be below how many minutes?

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What is considered an outbreak? How to investigate a disease outbreak? Your paper should be 3-4 pages in length

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the​ drug, 28 subjects had a mean wake time of 96.9 min and a standard deviation of 42.3 min. Assume that the 28 sample values appear to be from a normally distributed population and construct a 98​% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is​ effective? Find the confidence interval estimate. nothing minless thansigmaless than nothing min ​(Round to two decimal places as​ needed.)

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 1.01.0 literliter and a standard deviation of 0.040.04 liter. Suppose you select a random sample of 2525 bottles. a. What is the probability that the sample mean will be between 0.990.99 and 1.01.0 literliter​? b. What is the probability that the sample mean will be below 0.980.98 literliter​? c. What is the probability that the sample mean will be greater than 1.011.01 ​liters? d. The probability is 9999​% that the sample mean amount of soft drink will be at least how​ much? e. The probability is 9999​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)? a. The probability is nothing. ​(Round to three decimal places as​ needed.) b. The probability is nothing. ​(Round to three decimal places as​ needed.) c. The probability is nothing. ​(Round to three decimal places as​ needed.) d. There is a 9999​% probability that the sample mean amount of soft drink will be at least nothing ​liter(s). ​(Round to three decimal places as​ needed.) e. There is a 9999​% probability that the sample mean amount of soft drink will be between nothing ​liter(s) and nothing ​liter(s). ​(Round to three decimal places as needed. Use ascending​ order.)

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The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of woman receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in table #10.1.8.

a.) Test at the 5% level for a correlation between percentages spent on health expenditure and the percentage of woman receiving prenatal care.

b.) Find the standard error of the estimate.

c.) Compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure.

1. Over a very long period of time, a sheriff determines the mean vehicle speed on a road is 67 miles per hour, the standard deviation is 3 miles per hour. Treat this as the population, not a sample.
   1. If the speed limit is 60 miles per hour, what percentage of the vehicles exceed the speed limit?
   2. The sheriff cracks down on speeders. His deputies ignore any vehicles going less than 63 mph, and issue warnings to those going between 63 and 65, and issue tickets to those going faster than 65 mph.
      1. What percentage will get warnings?
      2. What percentage will get tickets?

Following the crackdown, the sheriff takes a random sample (n=84) of vehicle speeds on the road way. His sample data: mean is 63 mph, sample SD is 4 mph.

3. Calculate the standard error of the sample mean using the sample standard deviation, and applying the +/- 2 rule of thumb, calculate the 95% confidence interval around the sample mean
4. A county commissioner claims that the crackdown had no effect, and the average speed is still 67 mph. Is this commissioner correct?
   1. How likely is it that the sample of came from a population where the average speed is 67?
5. What if the sheriff’s post-crackdown random sample was not n=84 but in fact n=30? Assume the sample mean and standard deviation were unchanged. Use a t-table to determine the 95% confidence interval around that sample mean.
   1. Would the county commissioner be accurate in this case?

1.) The file cats.csv contains a data set consisting of the body weight (in kilograms) and heart weight (in grams) for 12 cats. Test at the 5% significance level that a positive linear relationship exists between the body weight of cat and their mean heart weight. Provides all parts of the test including hypotheses, test statistic, p-value, decision, and interpretation.

2.) The file cats.csv contains a data set consisting of the body weight (in kilograms) and heart weight (in grams) for 12 cats. Construct and interpret a 90% confidence interval for β1

cats.csv file is

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twelve 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution

The probability in part (b) is much higher because the mean is smaller for the x distribution.

1.) The file cats.csv contains a data set consisting of the body weight (in kilograms) and heart weight (in grams) for 12 cats. Give the estimated regression line using the body weight as the predictor variable (x-variable) and the heart weight as the response variable (y-variable). Also, provide interpretations in terms of the problem for the slope and the y-intercept.

2.) The file cats.csv contains a data set consisting of the body weight (in kilograms) and heart weight (in grams) for 12 cats. Give the correlation coefficient and the coefficient of determination. Provide interpretations for both of these.

3.) The file cats.csv contains a data set consisting of the body weight (in kilograms) and heart weight (in grams) for 12 cats. Give the point estimate and 99% confidence interval for the mean heart weight of cats whose body weights are 2.4 kilograms. Give an interpretation for the 99% confidence interval.

cats.csv file is

An economist is studying the job market in denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods Gave the following information (units in hundreds of jobs).

x 15 35 48 28 50 25

y 3 4 7 5 9 3

complete parts (a) through (e), given ∑x=201, ∑y=31, ∑x2=7663, ∑y2=189, ∑xy=1186, and r≈0,901.

a)draw a scatter diagram displaying the data

b) verify the given sums, ∑x, ∑y, ∑x2, ∑y2, ∑xy, and the value of the sample correlation coefficient r. ()round your value for r to three decimal value).

c) find the x-, and y- then find the equation of the least-squares line yˆ=a+bx. (round your answers for x- and y- to two decimal places. round your answers for a and b to three decimal places.)

e)find the value of the coefficient of determination r2. what percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? what percentage is unexplained? (round your answer for r2 ro three decimal places. round your answers for the percentages to one decimal places.)

f) for a neighborhood with x=37 hundred jobs, how many are predicted to be entry level jobs? (round your answer to two decimal places.)

I have Standard Deviation and Mean of 2 sets of data.
Based on the data, how can we infer at the 5% significance level that the score of individuals in the 4th year is better than the individuals in 1st year?

The sample size is 430

What distribution should be used to model variance? Why?