Statistic for business Assignment 1 first semester 2020-2021 ( upload for pre) PDF

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ASSIGNMENT COVER SHEETSTUDENT DETAILS Student name: Lê VinhStudent ID number: 31211021898UNIT AND TUTORIAL DETAILS Unit name: Statistic for businessUnit number: SB-DH47ISB- Tutorial/Lecture: Class day and time: Thursday, 15: Lecturer or Tutor name: Lê Văn ChơnASSIGNMENT DETAILSTitle: Stat assignment...

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ASSIGNMENT COVER SHEET STUDENT DETAILS Student name: Lê Vinh

Student ID number:

UNIT AND TUTORIAL DETAILS Unit name: Statistic for business Tutorial/Lecture: Lecturer or Tutor name:

31211021898

Unit number:

SB-DH47ISB-8

Class day and time: Thursday, 15:30

Lê Văn Chơn

ASSIGNMENT DETAILS Title: Length :

Stat assignment 2 Due date:

5/01/2022

Date submitted:

4/01/2022

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SB Assignment 2 Chapter 6 6.26 J.D. Power and Associates says that 60 percent of car buyers now use the Internet for research and price comparisons. (a) Find the probability that in a sample of 8 car buyers, all 8 will use the Internet. (b) at least 5. (c) more than 4. (d) Find the mean and standard deviation of the probability distribution. (e) Sketch the PDF (using Excel or Appendix A) and describe its appearance (e.g., skewness). (Data are from J. Paul Peter and Jerry C. Olson, Consumer Behavior and Marketing Strategy, 7th ed. [McGraw-Hill/Irwin, 2005], p. 188.) a) We have Among a sample of 8 car buyers, all of them will use the internet is : = b) The probability of at least 5 out of 8 will use the internet:

c) The probability of more than 4 out of 8 will use the internet is: d) Mean:

e) Sketch the PDF (using Excel or Appendix A) and describe its appearance (e.g., skewness). PDF of binomial distribution According to Appendix A

x 0 1 2 3 4 5 6 7 8

P(X=x) 0.0007 0.0079 0.0413 0.1239 0.2322 0.2787 0.2090 0.0896 0.0168

6.77 A small feeder airline knows that the probability is .10 that a reservation holder will not show up for its daily 7:15 a.m. flight into a hub airport. The flight carries 10 passengers. (a) If the flight is fully booked, what is the probability that all those with reservations will show up? (b) If the airline overbooks by selling 11 seats, what is the probability that no one will have to be bumped? (c) That more than one passenger will be bumped? *(d) The airline wants to overbook the flight by enough seats to ensure a 95 percent chance that the flight will be full, even if some passengers may be bumped. How many seats would it sell? a) This is binomial distribution because it has 2 outcomes: will and will not show up for the flight. ( n=10 ( passengers)). X= number of passengers showing up for the flight P( wont show ) =0.1  P( show )= 1 - P( wont show ) = 1-0.1=0.9  If the flight is fully booked, the probability that all with reservations will show up is b) If the airline overbooks by selling 11 seats => n=11 The probability that no one will be bumped is the probability that no one will show up late

c) The airplane has 10 seats, but it overbooks by selling 11 of them. Therefore, only the 11th passenger showing up will be bumped. Thus, there will be no more than 1 customer be bumped since there are only maximum 11 booked seats.

Chapter 7 7.37 The weights of newborn babies in Foxboro Hospital are normally distributed with a mean of 6.9 pounds and a standard deviation of 1.2 pounds. (a) How unusual is a baby weighing 8.0 pounds or more? (b) What would be the 90th percentile for birth weight? (c) Within what range would the middle 95 percent of birth weights lie? a) X= the newborn babies’ weights,

Standardize: CDF table of standard normal distribution

b) The 90th percentile for birth weight is CDF table of standard normal distribution

  The percentile is 90th so z=1.29 c) The interval that the middle 95 percent of birth weight lie is ( 6.9 – t, 6.9 + t)

X = 4.55 lbs to 9.25 lbs

7.60. A passenger metal detector at Chicago’s Midway Airport gives an alarm 0.5 time a minute. (a) Find the median waiting time until the next alarm. (b) Find the first quartile of waiting time before the next alarm. (c) Find the 30th percentile waiting time until the next alarm.

Show all calculations clearly. a) Alarm every 5 minutes => X=waiting time until next alarm (minutes) Exponential distribution XExponential(0.5) Median (second quartile Q2) So =0.5 =>  -(0.5) x=ln(0.5)  X=1.3863 minutes  Second quartile Q2 is 1,3863 minutes b) First quartile Q1

 57536  First quartile Q1 is 0,57536 minutes. c) 30th percentile is     71335 minutes The 30th percentile is 0.71335 minutes.

Chapter 8 8.16 Guest ages at a Vail Resorts ski mountain typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5 years. (a) Even though the population distribution of age is rightskewed, what will be the shape of the distribution of − X , the average age, in a random sample of 40 guests? (b) From a random sample of 40 guests, the sample mean is 36.4 years. Calculate a 99 percent confidence interval for μ, the true mean age of Vail Resorts ski mountain guests

a) According to Central Limit Theorem, since the sample size is 40 ( , the sampling distribution of is normal b) Sample size n=40, sample mean Population standard deviation We have 

Chapter 9 9.18The mean potassium content of a popular sports drink is listed as 140 mg in a 32oz bottle. Analysis of 20 bottles indicates a sample mean of 139.4 mg. (a) Write the hypotheses for a two-tailed test of the claimed potassium content. (b) Assuming a known standard deviation of 2.00 mg, calculate the z test statistic to test the manufacturer’s claim. (c) At the 10 percent level of significance (α 5 .10), does the sample contradict the manufacturer’s claim? (d) Find the p-value a) Two-tailed test of the potassium content : Null hypothesis: Alternative hypothesis: b)

Test statistic:

C) CDF table for standard normal distribution for critical value C95%= 1.65 As  Do not reject the hypothesis at 10% level d) P-value :

9.39 According to J.D. Power & Associates, the mean purchase price of a smartphone device (such as an iPhone or Blackberry) in 2008 was $216. In 2009, a random sample of 20 business managers who owned a smartphone device showed a mean purchase price of $209 with a sample standard deviation of $13. (a) At α 5 .05, has the mean purchase price decreased? State the hypotheses and decision rule clearly. (b) Use Excel to find the p-value and interpret it. a) One tailed test: Null hypothesis: Alternative hypothesis: E.g n=20,

Search the CDF table for t distribution for critical value C95% C95%= 1,729 Test statistic: As Reject null hypothesis at 5% level b) p-value = T.DIST (-2,408;19; TRUE) = 0.0138 P-value smaller than 0.05, also reject null hypothesis at 5% level....