The accompanying data represent the pulse rates​ (beats per​ minute) of nine students. Treat the nine students as a population. Compute the​ z-scores for all the students. Compute the mean and standard deviation of these​ z-scores. Compute the​ z-scores for all the students. Complete the table.

Student 1 .

Student 2

Student 3

Student 4

Student 5

Student6

Student 7

Student 8

Student 9

​(Round to the nearest hundredth as​ needed.) Compute the mean of these​ z-scores.

The mean of the​ z-scores is _____

. ​(Round to the nearest tenth as​ needed.)

Compute the standard deviation of these​ z-scores. The standard deviation of the​ z-scores is ____

. ​(Round to the nearest tenth as​ needed.) Enter your answer in each of the answer boxes.

Pulse Rates Student Pulse

Student 1    77

Student 2    61

Student 3    60

Student 4    80

Student 5    73

Student 6    80

Student 7 80

Student 8    68

Student 9    73

Should the following pairs of events be modeled as independent or dependent? Explain your reasoning.

(a) We choose a voter at random (all voters equally likely) from Minneapolis. Let A be the event that the

voter favors the mayor, and B be the event that the voter favors the police chief.

(b) Two people are selected at random from Minneapolis. Let A be the event that the first person favors

the mayor, while B is the event that the 2nd person favors the mayor.

(c) Flip a coin and let A be the event that the coin is heads, and B be the event that the coin is tails.

(d) A person is selected at random from Minneapolis. Let A be the event that the person likes the movie "The

Incredibles", while B is the event that the person likes "The Incredibles 2."

You are given the following LP model in algebraic form, with x₁ and x₂ as the decision variables:

Minimize Cost = 40x₁ + 50x₂

Subject to

                Constraint 1: 2x₁ + 3x₂ >= 30,

                Constraint 2: x₁ + x₂ >= 12,

                Constraint 3: 2x₁ + x₂ >= 20,

and x₁ >=0, x₂ >= 0.

1. Use the graphical method to solve this model.
2. How does the optimal solution change if the objective function is changed to

Cost = 40x₁ + 70x₂?

3. How does the optimal solution change if the third functional constraint is changed to

2x₁ + x₂ >= 15?

Please graph feasible region for part a

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n =928 and x=581 who said​ "yes." Use a 99% confidence level.

A. Find the best point of estimate of the population of portion p.

B. Identify the value of the margin of error E. (round to five decimal places as needed.)

C. Construct the confidence interval. _ < p <_ round to four decimal places.

D. Write a statement that correctly interprets the confidence interval.

In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 7 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet.

(a) Make a histogram of the probability distribution of r.

(b) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(c) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(d) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days

(e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days

(f) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)

---Select--- Yes No , because the probability of at least 1 day with surf of at least 6 feet is  and the expected number of days when the surf will be at least 6 feet is  ---Select--- less than equal to greater than one.

Continuous data sets can be analyzed for measures of central tendency, dispersion, and quartiles. Discuss the importance of reviewing these measures and identify the full story that these measures reveal about the data that is relevant to the business. Provide a relevant example to illustrate your ideas. In replies to peers, discuss whether you agree or disagree with the examples provided and justify your ideas.

Consider the following time series data:

Month 1 2 3 4 5 6 7

Value 23 15 20 12 18 22 15

Work Exercises 1 and 2 using the formula for the probability density function and a hand calculator. Do not use EXCEL. Show all of your work.

1. Assume 45% of all persons three years of age and older wear glasses or contact lenses, For a randomly selected group of seven people, what is the probability that
   1. Exactly 3 wear glasses or contact lenses?
   2. At least 3 wear glasses or contact lenses?
   3. At most 5 wear glasses or contact lenses?
   4. Between 2 and 6 wear glasses or contact lenses?

2. Assume 75% of youths 12-17 years of age have a systolic blood pressure less than 136 mm of mercury. What is the probability that a sample of 12 youths of that age will include
   1. Exactly 8 who have systolic blood pressure less than 136?
   2. Less than 10 who have systolic blood pressure less than 136?
   3. At least 10 who have systolic blood pressure less than 136?
   4. Between 5 and 8 who have systolic blood pressure less than 136?

3. Use EXCEL to complete the entries in the following table. Assume
   1. X represents the number of current cigarette smokers in a sample of size 10.
   2. Each selected subject has a 25% of being a current cigarette smoker.
   3. Being a current cigarette smoker is independent for all subjects

Let P(A) = 0.40, P(B) = 0.20, P(C) = 0.50, P(D) = 0.30, P(A ∩ B) = 0.15, P(A | C) = 0.60, P(B | C) = 0.20, P(B ∩ D) = 0.10, and C and D are mutually exclusive.

Find ...

a. P(C ∩ D)

b. P(C U D)

c. P(B ∩ C)

d. Which one of the following pairs is a pair of statistically independent events? (A and C) (B and D) (B and C) (C and D)

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 3.1 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

(a) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)


(b) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)


(c) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 10 feet per year and σ = 2.7 feet per year.

Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 7 years


(b) an escape dune will move a total distance of less than 80 feet in 7 years


(c) an escape dune will move a total distance of between 80 and 90 feet in 7 years

Here is the dataset containing plant growth measurements of plants grown in solutions of commonly-found chemicals in roadway runoff. Researchers wish to determine roadway runoff with different compositions has a different effect on plant growth.

Phragmites australis, a fast-growing non-native grass common to roadsides and disturbed wetlands of Tidewater Virginia, was grown in a greenhouse and watered with one of the following treatments:

• Distilled water (control);
• A weak petroleum solution (representing standard roadway runoff);
• Sodium chloride solution;
• Magnesium chloride solution;
• De-icing brine (50% sodium chloride and 50% magnesium chloride).

Twenty grass preparations were used for each solution, and total growth (in cm) was recorded after watering every other day for 40 days.

1.) Perform the correct statistical test to determine the p-value.

• Report your answer in scientific notation
  • e.g. 1.00E-04

2.) Based on the p-value from your Phragmites dataset analysis, select the options that are TRUE.

3.) Which is / are (an) appropriate evaluation(s) of the results of your Phragmites data analysis?

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $47 and the estimated standard deviation is about $8.

(a) Consider a random sample of n = 80 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 47 and standard error σ_x = $0.89.The sampling distribution of x is not normal.    The sampling distribution of x is approximately normal with mean μ_x = 47 and standard error σ_x = $0.10.The sampling distribution of x is approximately normal with mean μ_x = 47 and standard error σ_x = $8.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has an approximately normal distribution.

It is not necessary to make any assumption about the x distribution because μ is large.   

It is necessary to assume that x has a large distribution.

It is not necessary to make any assumption about the x distribution because n is large.

(b) What is the probability that x is between $45 and $49? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $45 and $49? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 80 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The x distribution is approximately normal while the x distribution is not normal.

The standard deviation is larger for the x distribution than it is for the x distribution.    

The standard deviation is smaller for the x distribution than it is for the x distribution.

The sample size is smaller for the x distribution than it is for the x distribution.

The mean is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.

The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    

A company has sales of automobiles in the past three years as given in the table below. Using trend and seasonal components, predict the sales for each quarter of year 4.

Complete all of the steps to derive the normal equations for simple linear regression and then solve them.

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.

A. 0.8531

B. 0.9634

C. 0.9712

D. 0.9931