To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3700, and the average first-year commission for each new account opened is $5300. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account. Assume that the number of new accounts you get randomly is: Simulation Trial New Accounts :

Construct a spreadsheet simulation model to analyze the profitability of Gustin’s seminars. Round the answer for the expected profit to the nearest dollar. Round the answer for the probability of a loss to 2 decimal places. Enter minus sign for negative values. The expected profit from a seminar is ______$ and there is a probability of a_______loss. Would you recommend that Gustin continue running the seminars? . How large of an audience does Gustin need before a seminar’s expected profit is greater than zero? Use Trial-and-error method to answer the question. Round your answer to the nearest whole number. ______attendees

The Environmental Protection agency requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individually trucks according to a Normal distribution with mean 1.45 grams per mile driven and standard deviation 0.40 grams per mile.

(a) What is the 66th percentile for NOX exhaust, rounded to four decimal places?

(b) Find the interquartile range for the distribution of NOX levels in the exhaust of trucks rounded to four decimal places.

28)

The weight of adult koalas living in a particular region is normally distributed with a mean of 21.1 pounds and a standard deviation of 3.24 pounds. A sample of 6 adult koalas from the region is selected at random.

Find the probability that the mean weight of koalas in the sample is within 0.6 pounds of the population mean weight.

Round your answer to 4 decimal places.

Please explain each step in detail.

Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean μμ =125 and standard deviation σσ =14.

Create an empirical rule graph with the following:

• A title and label for the horizontal axis including units.
• Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis
• Labels for the areas of the 8 regions separated by the vertical lines as well.

Note: This may be hand drawn or computer generated. See the models for desired formats.

a. Upload your completed file below. Choose FileScan Mar 5, 2020 (1).pdf

Now use your graph to answer the following questions.

b. About 95% of men will have blood pressure between what amounts?

and

c. What percentage of men will have a systolic blood pressure outside the range 97 mm to 167 mm?

d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 172 mm. Use statistics to explain the gravity of his situation. Structure your essay as follows:

1. A brief description of the normal distribution.
2. Why the normal distribution might apply to this situation.
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. A brief description of the empirical rule
5. What region of the graph (drawn in part a) the individual falls in
6. An estimate of individual's percentile.
7. Why this signifies a health concern.
8. A suggested course of action.

Based on a random sample of 25 units of product X, the average weight is 104 lbs., and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. At alpha = .01. What is the calculated value of the test statistic? Construct the hypotheses according to the question and perform the test at 1% significance level.

The following data represent the commute time​ (in minutes) x and a score on a​ well-being survey y. The equation of the​ least-squares regression line is ModifyingAbove y with caret equals negative 0.0522 x plus 69.3800 and the standard error of the estimate is 0.3295. Complete parts ​(a) through ​(e) below.    x 10 20 30 40 55 77 110    y 69.0 68.3 67.9 67.1 66.1 65.9 63.5 ​(a) Predict the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​ needed.) ​(b) Construct a​ 90% confidence interval for the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.) ​(c) Predict the​ well-being index composite score of​ Jane, whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​ needed.) ​(d) Construct a​ 90% prediction interval for the​ well-being index composite score of​ Jane, whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.) ​(e) What is the difference between the predictions made in parts​ (a) and​ (c)? A. The prediction made in part​ (a) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 35 ​minutes, and the prediction made in part​ (c) is an estimate of the mean​ well-being score for all individuals whose commute is 35 minutes. B. The prediction made in part​ (a) is an estimate of the mean​ well-being score for all individuals whose commute is 35 ​minutes, and the prediction made in part​ (c) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 35 minutes. C. The prediction made in part​ (a) is the average​ well-being score for all individuals whose commute is 67.55 ​minutes, and the prediction made in part​ (c) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 67.55 minutes.

Someone is dealt a 6 card hand. Find the number of hands that fit in the following descriptions.

a) The cards are all red.

b) exactly four of the cards are clubs

c) Either three or four of the cards are face cards

d) There are at most four diamond cards in the hand

e) There are exactly two hearts and three diamonds in the hand

How many proper subsets are there for this set {A,B,C,D,E,F,G,H,I}?

A mail-order company claims that at least 60% of all orders are mailed within 48 hours. From time to time the quality control department at the company checks whether this promise is fulfilled. Recently the quality control department at this company took a sample of 400 orders and found that 208 of them were mailed within 48 hours of the placement of the orders. Testing at a 1% significance level, can you conclude that the company’s claim is true? Use both the critical value approach and the p-value approach.

Problem 9-11 (Algorithmic)

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1050 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier?

What is the total purchase cost for the components?

$  

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 13 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of W_q for each alternative.

1. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 29 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations
2. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 20 customers per hour for each server. Note: Use P₀ values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations.

Consider a homogeneous Poisson process {N(t), t ≥ 0} with rate α. Now color each point blue with probability p and red with probability q = 1 − p. Colors of distinct points are independent.

Let B₂ be the location of the 2nd blue point. Find E(B₂).

QUESTION

The table below shows data collected over a two-hundred-year time span in a woodland area. Each year, the number of new invasive species that appeared for the very first time in that woodland was recorded. Do new invasive species appear in random years, or non-random years? If they appear randomly, the data should follow a Poisson distribution.

1. Calculate the mean number of new invasive species per year
2. Test whether the data fit a Poisson distribution, making sure the data meet the assumptions of a Chi-square goodness-of-fit test.

nStandard methodology for a single sample mean can be used to calculate a confidence interval for the slope of the least‑squares line and to test hypotheses other than H₀: ß₁= 0. In both cases, one needs to have an estimate of the slope and of its standard deviation (sometimes called standard error). Furthermore, one needs to recognize that the degrees of freedom for the standard deviation is the same as the error degrees of freedom (n ‑ 2).

Note that the EXCEL gives the standard error of estimate directly, but correctly calls it the standard deviation of the slope. Therefore, you must not divide by the square root of sample sizeas in example 16.

Use the above information to calculate a 90% confidence interval for the slope of the true regression line. For 30 degrees of freedom and a= 0.1, the critical t‑value is 1.697.

       (i.e. slope + margin of error)

nUse this same information to calculate a statistic to test the null hypothesis H₀: ß₁= 0.05 against a one‑sided alternative H₁: ß₁> 0.05. Use a 1 percent significance level (for which the critical value is 2.423).

            Reminder:  t = estimated value - hypothesized value  =   slope -  0.05

                                    standard error (deviation) of estimate        st dev of slope

I had recently conducted an experiment: the moment the fuel light in my car goes on, I will find a closest gas station to fill up the tank. But the number of gallons needed to fill up are all over the place. This makes me wonder: 1) how can we verify it is actually one gallon when the pump says it pumps one gallon of gas into your car, 2) if we know some gas stations are short selling us, how to find out what the true volume of gas is.

These two problems are known as hypothesis testing (testing the claim, i.e., the hypothesis, that a supposed gallon is indeed one gallon), and estimation (estimating the true volume) in statistical inference. They are a lot more complex than they might appear because of the nature of continuous variables.

Since the volume is measured, i.e., a continuous variable, you know if you take a measure of the volume of a supposed gallon of gas pumped out the of machine, it will never be exactly 1.0000000... gallon.

So if it turns out to be 0.9823, can you say they are cheating?

You might say I will take 30 measures and look at their mean, but again if it turns out to be 0.9912? can you say they are cheating?

1. Outline your thoughts and share. The statistical inference on modern stat textbooks are the results of two statisticians's answer (Fisher's p-value and Neyman's critical values) to these questions, and they are not even in full agreement. So don't feel bad if you can't solve them in 1 hour. However, the more thoughts you put into this, the less challenging you will find the answers provided in the next two sections.