Use Excel to Answer.

A random sample of six cars from a particular model year had the fuel consumption figures, measure in miles per gallon, shown below.

1. Using T.INV, find a 90% confidence interval for the population mean of fuel consumption for cars of this model year. Assume the distribution is normal.   (Round to 2 digits, since our raw data below are expressed with one digit.) (Show work in space provided.)

(ii) Calculate the same interval using CONFIDENCE.T. (Show work in space provided.)

(iii) Calculate the same interval using T.INV.2T.

(Note: when calculating the lower and upper bounds of the interval, do not use a rounded mean that you’ve calculated with AVERAGE. Use the unrounded mean.   Round only the final answers, which are the lower and upper bounds of the interval. Also, make sure to use STDEV.S to calculate the sample standard deviation.)

              Data:

              28.6

              18.4

              19.2

              25.8

              19.4

              20.5

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster three centers, five guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] Correct: Your answer is correct. lineups (b) Now suppose the roster has 3 guards, 5 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 13 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

Multi part question needing assistance please.

1. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.378°C. P(Z>−1.378) _____________ ******* WHAT DO I DO ABOUT THE 8? I CAN SEE ON THE CHART THE -1.37 BUT DONT KNOW WHAT TO DO CONCERNING THE 8.

2. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 1.141°C and 2.549°C. P(1.141<Z<2.549) _______ ****HOW DO I DO TWO GIVEN NUMBERS?

3. About % of the area under the curve of the standard normal distribution is between z=−2.159 and z=2.159 (or within 2.159 standard deviations of the mean).

The following xbar and s charts based on n=4 have shown statistical control: Xba Chart: UCL=710, CL=700, LCL=690, s chart- UCL=18.08, CL=7.979, LCL=0,

A)Estimate the process parameters mean and sigma (standard deviation).

B)If the specifications are at 705+/-15, and the process output is normally distributed, estimate the fraction non conforming.

C)For the Xbar chart, find the probability of a type I error, assuming sigma is constant.

D)Suppose the process mean shifts to 693 and the standard deviation simulatneously shifts to 12. Find the probability of detecting this shift on the x bar chart on the first subsequent sample.

E)For the shift of part (D) , find the ARL.

1. 5.232608753	51.33997	1
   4.559347708	3.047033	0
   4.550088246	11.71957	1
   3.386566659	28.04548	1
   0.989064618	0.202602	0
   4.555668273	67.83218	1
   4.186405129	53.06328	1
   1.207150769	78.43352	0
   3.445792543	14.46725	1
   2.962975266	23.10411	0
   0.173612404	65.70817	0
   2.768815371	65.28198	1
   2.747367434	97.82201	1
   4.486882933	77.4523	1
   4.824678695	0.743551	0
   5.586206724	48.65186	1
   2.755386381	73.45392	1
   1.787901977	97.36504	1
   5.951385802	90.85691	1
   2.737556923	15.44293	0
   5.408894983	4.157112	0
   1.715859824	0.937882	0
   1.278844906	74.59771	0
   2.514277044	97.32341	1
   3.187058008	38.67714	1
   4.949777159	87.91089	1
   5.948802076	99.45704	1
   4.58854855	73.22006	1
   4.944593251	2.002865	0
   4.095092929	30.82503	1
   1.580255616	81.42979	1
   5.582168688	77.37155	1
   1.409875297	73.8556	1
   4.173571574	10.78412	0
   3.405384527	76.08957	1
   5.303746588	91.13028	1
   2.646338619	30.76739	0
   5.648448558	24.47563	0
   5.460162608	6.448907	1
   2.530400279	92.75311	1
   5.282410782	26.05696	1
   4.798709185	42.12116	1
   4.300055705	57.20119	1
   4.729502404	6.523547	0
   2.476612604	55.6309	1
   3.190133005	67.05927	1
   1.021463153	77.07357	1
   0.733750098	95.86227	1
   2.724156232	4.533329	0
   4.232730005	96.12467	1

   For a column of data x and a column of data y, there is an equation that relates the slope of the line of best fit (m) with the correlation coefficient (r). That equation is:

m = r * std(y)/std(x)

In the equation above, std(y) represents the standard deviation of the y column of data and std(x) is the standard deviation of the x column of data.

Use the Pandas .corr() and .std() methods to compute the slope of the line of best fit between Diameter and Pigment（first & second col）.

Next, use compute the y-intecept of the line of best fit using:

b = ybar – m*xbar

         Lastly, plot the line of best fit using matplotlib.pyplot.

6 a) You and your friend are in a class with 12 students. For a project, the class is randomly divided into two equal groups. “Randomly” means all divisions are equally likely. What is the probability that you and your friend end up in the same group?

6 b) Revisit part a). Calculate the probability that you and your friend will end up in the same group if the class is divided into three equal groups instead.

Suppose that you want to improve the process of loading passengers onto an airplane. Would a discrete event simulation model of this process be useful? What data would have to be collected to build this model?

Investment advisors might subscribe to the Business Times (BT) or Straits Times (ST). For those investment advisors who subscribe to at least one of the papers, one-third subscribe to only one newspaper, ST, and one-fourth subscribe to only one newspaper, BT. 40% of the investment advisors subscribe to both papers. (a) Complete the probability table below (the grey boxes).

BT BTC TOTAL

ST

STC

TOTAL 1

Total 1.0 (b) Suppose an investment advisor receives at least one of the papers. What is the probability they receive the BT?

The Hillsboro Aquatic Centre has an indoor pool with lanes for lap swimming and an open area for recreational swimming and various exercise and water aerobics programs. From 1 June to mid-August it operates on a summer schedule, and from mid-August to the end of May it operates according to normal weekday and weekend schedules. The centre’s policy for the pool is to have a lifeguard-to-patron ratio of 1:40. The centre director wants to develop a forecast of pool attendance for the weekday schedule in order to determine the number of lifeguards to hire. The following data for average daily attendance for each hour of the day that the pool is open to the public (i.e., there are no swim team practices):

Develop a seasonally adjusted forecast model for these data for hourly pool attendance. Forecast attendance for each hour for year 7 by using a linear trend line estimate for pool attendance in year 7. Do the data appear to have a seasonal pattern?

The government conducts a survey of the population and finds that 208 of 681 respondents report voting for party A last election, and 284 of 512 respondents report voting for party A for the next election. If you are conducting a hypothesis testing with a null hypothesis of p1=p2{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mo>=</mo><msub><mi>p</mi><mn>2</mn></msub></math>"}, calculate p{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>p</mi></menclose></math>"} .

An insurance company issues a one-year $1,000 policy insuring against an occurrence A that historically happens to 3 out of every 100 owners of the policy. Administrative fees are $25 per policy and are not part of the company's "profit." How much should the company charge for the policy if it requires that the expected profit per policy be $60? [HINT: If C is the premium for the policy, the company's "profit" is C − 25 if A does not occur, and C − 25 − 1,000 if A does occur.]

=$?

3.2

Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing time to failure (in hours) at 90% breaking strength.

(a) Find the range.


(b) Use a calculator to calculate Σx and Σx². (Round your answers to two decimal places.)

(c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to two decimal places.)

(d) Use the results of part (c) to compute the coefficient of variation. (Round your answer to the nearest whole number.)
%

What does this number say about time to failure?

The standard deviation of the time to failure is just slightly smaller than the average time.The coefficient of variation says nothing about time to failure.    The standard deviation of the time to failure is just slightly larger than the average time.The standard deviation is equal to the average.

Why does a small CV indicate more consistent data, whereas a larger CV indicates less consistent data? Explain.

A small CV indicates more consistent data because the value of s in the numerator is smaller.A small CV indicates more consistent data because the value of s in the numerator is larger.    

Consider sample data with

x = 8

and

s = 2.

(a) Compute the coefficient of variation.


(b) Compute a 75% Chebyshev interval around the sample mean.

1. Acompanysellinglicensesofnewe-commercesoftwareadvertisedthatfirmsusingthissoftware could obtain, on average during the first year, a minimum yield (in cost savings) of 20 percent on average on their software investment. To disprove the claim, we checked with 10 different firms which used the software. These firms reported the following cost-saving yields (in percent) during the first year of their operations:

   {17.0, 19.2, 21.5, 18.6, 22.1, 14.9, 18.4, 20.1, 19.4, 18.9}.

   1. Do we have significant evidence to show that the software company’s claim of a minimum of 20 percent in cost savings was not valid? Test using α = 0.05.

   2. Compute a 95% confidence interval for the average cost-saving yield estimate.

You are Susan Dean, a 35 year old woman who has always been interested in owning your own business. You graduated from Gorham HS, attended SMCC, eventually transferring to USM where you earned a bachelor’s degree in Business with a major in Marketing. Eventually you went to graduate school and earned a Master’s of Business Administration (MBA). For the last 10 years you have worked as a marketing specialist/management specialist with Yum! Brands, Inc. where you helped management open several Taco Bells and Pizza Huts in southern Maine. In addition, you evaluated several underperforming stores that had to be closed. After contacting several major corporations you find that McDonalds is the only major brand looking to open another store in the town of Gorham near the USM campus. There is a Burger King in the area. You in fact actually worked at McDonalds when you were a youngster. You have decided that you would like to open a McDonald’s franchise in this area near USM. Your grandparents have left you with a significant amount of money for which you are grateful. You would like to use this towards your new business adventure. But you will need to finance the remaining balance. You apply for a business loan to a local bank. The bank requires you to submit a detailed business plan. This business plan will include projections for operating costs, revenue stream, profits, human resource needs, your business strategy, etc. There are multiple topics that have to be analyzed and for which projections have to be made. Because of this you will have to conduct a survey(s) in the Gorham region to assess multiple demographic, supply/demand issues, and other topics.

Discussion Question/Directions:

You are Susan Dean. You need to discuss issues for which you think a statistical study would be helpful (in obtaining the information needed for your business plan). his could be demographic information, assessing the desire for a McDonald’s in the region, traffic studies, household make up, what the projected demand would be, etc. There are hundreds of topics to zero in on. What topics do you think are important to know before you invest your money into such an important undertaking? What type of statistical study should be done? What types of data will you need to collect? How will you collect your data? How much do you think it will cost to gather your information?