Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that

NOTE: I'd like to learn how to do this in the shortest way possible on ti 84 plus calculator.

a) x>43

b) x<42

c) x>57.5

d) 42 <x<48

e) x<40 or x>55

f) 5% of the values are less than what X value?

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

h) 85% of the values will be above what X value?

Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon’s management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. Find the optimal solution. Give the number of call-center employees that exceed the minimum required. Use a software package LINGO or Excel Solver. If your answer is zero, enter "0".

Let X_i = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday…)

Solution:

Number of excess employees:

Total Number of Employees = ______

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Romans sells the Regular blend for $3.60 per pound and the DeCaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1000 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a plus sign before the blank. (Example: -300)

What is the optimal solution and what is the contribution to profit? If required, round your answer to the nearest whole number.

Optimal solution:

If required, round your answer to the nearest cent.

Value of the optimal solution = $ ______

True or false

1.T or F:A numerical variable is continuous if it’s possible values correspond to isolated points
on the number line.

2.T or F:A control group provides a baseline for comparison with a treatment group.
3.T or F: A unimodal set of data is one that contains only one variable.
T or F: When using histograms to compare groups of different sizes, one may use either
frequencies or relative frequencies for the vertical axis and still be effective.

4.T or F:One disadvantage of using the mean as a measure of center for a data set is that its
value can be affected by the presence of even a single outlier in the data set.

5.T or F:he interquartile range is a measure of spread in a set of data.
T or F: for any given data set, the median must be greater than or equal to the lower quartile,
and less than or equal to the upper quartile.

6.T or F: The standard deviation about the least squares line is roughly the typical amount by
which an observation deviates from the least squares line.
7.T or F :The interquartile range is resistant to the effect of outliers.
8.T or F:The correlation coefficient, r, does not depend on the units of measurement of the two
variables.

Question 6 options:

The length of western rattlesnakes are normally distributed with a mean of 60 inches and a standard deviation of 4 inches.

Enter answers as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.
Do not enter an answer as a percent.

Suppose a rattlesnake is found on a mountain trail:

a. What is the probability that the rattlesnakes' length will be equal to or less than 54.2 inches?

b. What is the probability its' length will be equal to or greater than 54.2 inches?

c. What is the probability that the rattlesnakes' length will be between 54.2 inches and 65.8 inches?

d. Suppose a nest of 16 rattlesnakes are found on the mountain trail:

What is the probability that the average length of the rattlesnakes will be 60.85 inches or more?

In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. Assume independence. (a) What is the probability that five or more people need to be tested to detect two with the gene? (b) What is the expected number of people to test to detect two with the gene?

Suppose that xt = wt + kwt−1 + kwt−2 + kwt−3 + · · · + kw0, for t > 0, k constant, and wi iid N(0, σ2w).

(a) Derive the mean and autocovariance function for {xt}. Is {xt} stationary?

(b) Derive the mean and autocovariance function for {∇xt}. Is {∇xt} stationary?

1. A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by gender: Men Women Total In Favor 1400 280 1680 Opposed 840 3080 3920 Total 2240 3360 5600 A) What is the probability of a randomly selected resident being a Man? B) What is the probability that a randomly selected resident is a Man and is Opposed to the bridge? C) What is the probability of a randomly selected resident being a Woman or Opposed to the bridge? D) If a randomly selected resident is a Man, what is the probability that he is Opposed to the bridge? E) Are gender and opinion about the bridge mutually exclusive events? Why? F) Are gender and opinion about the bridge independent events? Why? Show some "proof" with probabilities. 2. How many Combinations of 3 students can be selected from a group of 9 students? 3. Describe the Sample Space for the experiment of selecting one card from a deck of regular playing cards?

The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifacts†. Please show all steps to get answer. 85 45 120 80 75 55 65 60 65 95 90 70 75 65 68

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

x = cm

s = cm

(b) Compute a 90% confidence interval for the mean depth μ at which archaeological artifacts from the Wind Mountain excavation site can be found. (Round your answers to one decimal place.)

lower limit cm

upper limit cm

An urn contains 10 balls numbered 1 through 10. Five balls are drawn at random and without replacement. Let A be the event that “Exactly two odd-numbered balls are drawn and they occur on odd-numbered draws from the urn.” What is the probability of event A?

Please explain Thank you

What does regression analysis test?

A) Relationship between variables

B) Prediction of one variable based on another variable

C) Differences between variables

D) Slope of the regression line

Glenn Howell, vice president of standard insurance staff, has developed a new training program fully adaptable to the pace of users. new employees work in several stages at their own pace of work; the training term is given when the material is learned. The Howell program has been especially effective in accelerating the training process, since the salary of an employee during training is only 67% of what he would earn when completing the program. in recent years, the average term of the program has been 44 days, with a standard deviation of 12 days.

a) Find the probability that an employee will finish the program between 33 and 42 days.

b) What is the probability of finishing the program in less than 30 days?

c) To finish it in less than 25 or more than 60 days?

d) find the probability that an employee ends the program between 46 and 54 days.

e) find the probability that an employee ends the program between 41 and 50 days.

f) what is the probability of not finishing the program in 47 days?

Y is a Binomial random variable where, Y = The number of days in a week someone goes to the gym.

Where a week has 7 days and the probability of someone going to the gym on any given day is .65.  What is the probability that someone goes to the gym at least 3 days out of the week?

Hint: This is a cumulative probability, so you need to add up the probabilities of Y equaling all the possible values up to and including 3.

P(Y <= 3) = ?

(A) 0.2627

(B) 0.4694

(C) 0.3672

(D) 0.4718

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 17 35 53 28 50 25 y 2 4 6 5 9 3 Complete parts (a) through (e), given Σx = 208, Σy = 29, Σx2 = 8232, Σy2 = 171, Σxy = 1157, and r ≈ 0.855. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) For a neighborhood with x = 30 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) hundred jobs