The random variable x is normally distributed with a mean of 68 and a standard deviation of 4. Find the interquartile range (IQR)? Use R.

Assume that you have done two different studies on the same sample of people.

Explain how you could use z-scores to compare the data in one study with the data of the other.

What are some of the limitations or benefits of using z-scores to do this type of comparison?

LECTURE OF THE OPERATIONS RESEARCH I
You will randomly generate a linear programming model.
• Objective function should be a maximization problem.
• Model must have exactly three decision variables.
• Model must have two less-than equality (≤) constraints.
Please answer the following parts:
a) Take the dual of the primal problem you have on hand.
b) Solve the dual problem by using Graphical Solution Procedure. If the dual problem does not have a single optimal solution (or if the dual has unbounded/infeasible/multiple
optimal solution), go back to the starting point and change your initial model until you have one optimal solution for the dual problem.
c) By using the optimal dual solution, find the optimal primal problem by using Complementary Slackness Theorem. (Do not use Simplex Method to solve the primal problem. You must use complementary slackness theorem.)
d) Comment on the optimal solution of the primal problem. Calculate the values of slack variables. Which variables are basic at the optimal solution? Which variables are nonbasic
at the optimal solution?
e) For the basic variables at the optimal solution, create the optimal tableau by using matrix operations.

Investigate the effect of the term on simple interest amortized auto loans by finding the monthly payment and the total interest for a loan of $17,000 at

9

%

interest if the term is the following. (Round your answers to the nearest cent.)

(a) three years

(b) four years

(c) five years

Step by step

A company has two machines that produce widgets. The new machine produces 75% widgets and the older machine produces 25% widgets. Further, the new machine produces 10% defective widgets, while the older machine produces 30% defective widgets. If a widget is randomly selected what is the probability that it is defective?

1. Assume that a father of a teenager in the US is concerned about the number of crimes in schools that involve guns. After some investigation, he finds out that out of 320 crime reports in schools, 210 of the crimes involve a gun.

   1. Estimate with 90% confidence the proportion of crimes in schools that involve a gun.

   2. How many reports would this father need to find in order to be within 1 percentage point, with 95% confidence?

Calculate the covariance between variables X and Y. Is it a positive or negative relationship between the two variables?

b. Calculate correlation coefficient between X and Y. Is it a positive or negative relationship? Is it a strong linear, weak linear or nonlinear relationship between X and Y?

c. Use the Y data to calculate mean, range, standard deviation and variance.

d. Use the first Y value to calculate the Z-score. Is it an outlier?

e. Calculate the 60th percentile for the Y data.

Describe the steps of hypothesis testings. Develop a hypothesis and alternative hypothesis to be tested and describe how how you would apply these steps to your hypothesis.

A gasoline tank for a Honda Accord is engineered to hold 15 gallons of gas.  Gas tank capacity for a randomly selected Accord has an approximately normal distribution with mean 15.0 gallons and standard deviation of 0.1 gallons.

(a) What is the probability that a randomly selected Accord has a gas tank capacity within one standard deviation of the mean?

(b) What is the probability that a randomly selected tank will hold at most 14.85 gallons? Sketch a graph of this situation and shade the appropriate region.

(c) What is the probability that in the next twelve cars randomly selected, exactly four of those tanks will hold at most 14.85 gallons? Use your results from part (b).

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The Dubai traffic department believes that at least twenty-five percent of the drivers stopped on a given day are using their cell phones. Assume that a sample of 75 drivers were stopped on Friday and it was found that nine drivers in the sample were using their cell phones.

1. State the null and alternative hypotheses.

2. Test the hypotheses at the 5% significance level. What is the p-value of the test?

3. Do you have evidence to conclude that at least twenty-five percent of the drivers are using their cell

   phones?

4. Explain in words what the p-value you found in part b means/tells you.

5. What type of error you can commit here? What are the implications of this error?

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled, “The relation of dive duration (DD) to depth (D).” Duration DD is measured in minutes, and depth D is in meters. The report then says, “The regression equation for this bird is DD=2.69+0.0138D.

(a) What is the slope of the regression line? (Enter your answer rounded to four decimal places.)

slope = ?

(b) On average, if the depth of the dive increases by one meter, what is the increase in the diving duration? (Enter your answer rounded to four decimal places.)

increase in duration = ?minutes

(c) According to the regression line, how long does a typical dive to a depth of 189 meters last? (Enter your answer rounded to three decimal places.)

length of dive = ?minutes

Assume that the average amount of money spent on video games is normally distributed with a population standard deviation of 12.42 AED. Your friend wants to estimate the expenditure on video games, takes a sample of 10 students, and finds that the mean expenditure is 50.77 AED. a. Estimate with 99% confidence the average amount of expenditure on video games. b. How many students you need to sample in order to be within 5 AED, with 95% confidence? c. Assume that your friend told you that the average amount of expenditure from these 10 students should be at least 75 AED. Do you think he is correct? Explain using probabilities.

A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medical study is (2070, 2290). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 22 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.

The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? during each of the past 15 years, a polling organization has sur- veyed americans about their exercise habits. in the most recent of these polls, slightly over half of all american adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.

a. Construct a time series plot. does a linear trend appear to be present?

b. use simple linear regression to find the parameters for the line that minimizes mSe for this time series.

c. use the trend equation from part (b) to forecast the percentage of adults next year (year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week.

d. Would you feel comfortable using the trend equation from part (b) to forecast the percentage of adults three years from now (year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week?

Question
(a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257.
Calculate the unbiased estimator of the population variance.
(1 mark)

(b) Suppose the GPA of all students enrolled in a particular course can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Compute the probability that the
mean GPA of a random sample of 40 students selected from this course will be:

(i) lower than 3.2

(ii) between 3.3 and 3.6

(c) Suppose you throw a die 600 times. Apply a suitable technique to compute the
approximate probability of obtaining between 90 and 110 fours.