. Given the following probability distributions:
Distribution A Distribution B
X P(X) X P(X)
0 0.50 0 0.05
1 0.20 1 0.10
2 0.15 2 0.15
3 0.10 3 0.20
4 0.05 4 0.05
(a) Compute the expected value for each distribution.
(b) Compute the standard deviations for each distribution.
(c) Compare the results of distributions A and B.
5.3 How many credit card do you have in your wallet?According to a survey by Iposs, a large survey research company,26% of adults in the united states reported having no credit cards;38% reported having one or two;20% three or four;15% five or more;and 1% reported “not sure”.Suppose that the following table contains the complete probability distribution for the number of credit cards owned by adults in the united states:
Number of Credit Cards(X) p(
5.1. Given the following probability distributions: Distribution ADistribution B XP(X)XP(X) 00.5000.05 1 0.2010.10 20.1520.15 30.1030.20 40.0540.05 (a) Compute the expected value for each distribution. (b) Compute the standard deviations for each distribution. (c) Compare the results of distributions A and B. 5.3 How many credit card do you have in your wallet?According to a survey by Iposs, a large survey research company,26% of adults in the united states reported having no credit cards;38% reported having one or two;20% three or four;15% five or more;and 1% reported “not sure”.Suppose that the following table contains the complete probability distribution for the number of credit cards owned by adults in the united states: Number of Credit Cards(X)p(x) 0 0.26 1 0.22 2 0.16 3 0.12 4 0.08 5 0.06 6 0.04 7 0.03 8 0.02 9 0.01 (a)compute the mean number of credit cards owned by a u.s.adult. (b)compute the standard deviation. 5.20.Determine the following: (a)For n=4 and pie=0.12,what is P(X=0)? (b)For n=10 and pie=0.40,what is P(X=9)? © For n=10 and pie=0.50,what is P(X=8)? (d) For n=6 and pie=0.83,what is P(X=5)? 5.26 .You and two friends decided to go to McDonald’s. Instead, suppose that you went to KFC, which last month filled 87% the oders correctly. What is the probability that (a)all three orders will be filled correctly? (b)none of the three will be filled correctly ( c) at least two of the three will be filled correctly/ (D) What are the mean and standard deviations of the binomial distribution used in (a) through(c)? interpret these values. 6.1. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that A. Z is less than 1.57? B. Z is greater than 1.84? C. Z is between 1.57 and 1.84? D. Z is less than 1.57 or greater than 1.84? 6.5 Given a normal distribution with u = 100 and o = 10, what is the probability that A. X > 75? B. X< 70?="" c.="" x="">< 80="" or="" x=""> 110? D. 80% of the values are between what two X values (symmetrically distributed around the mean)? 6.10 A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8. A. What is the probability of getting a grade below 91 on this exam? B. What is the probability that a student scored between 65 and 89? C. The probability is 5% that a student taking the test scores higher than what grade? D. If the professor grades on a curve (i.e., gives A’s to the top 10% of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain. 6.14 Show that for a sample of n = 39, the smallest and largest Z values are – 1.96 and + 1.96, and the middle (i.e., 20th) Z value is 0.00. 6.19 The data in the file spending represent the per-capita spending, in thousands of dollars, for each state in 2004. Decide whether the data appear to be approximately normally distributed by A. Comparing data characteristics to theoretical properties. B. Constructing a normal probability plot. 7.1. For a population containing N=902 individuals what code number would you assign for (a)The first person on the list? (b) The fortieth person on the list? © The last person on the list? 7.4. For the study that consists of personal interviews with participants (rather than mail or phone surveys), explain why simple random sampling might be less practical than some other sampling methods. 7.8.Prenumbered sales invoices are kept in a sales journal.The invoices are numbered from 0001 to 5000. (a)beginning in row 16,column 1,and proceeding horizontally in Table E.1,select a sample of 50 invoice numbers. (b)select a systematic sample of 50 invoice numbers.Use the random numbers in row 20,columns 5-7 ,as the starting point for your selection. ©Are the invoices selected in (a) the same as those selected in(b)?why or why not? 7.10. “A survey indicates that the vast majority of college students own their own personal computers.”What information would you want to know before you accepted the results of this survey? 7.15.In may of 2007,one of the nation’s most respected cardiologists,Dr.steven nissen,reported his troubling analysis of the heavily prescribed diabetics drug Avandia.His analysis showed a 43% higher risk of heart attacks among patients taking Avandia,compared to other drugs used for the same condition.Furthermore,patients asking Avandia exhibited a 64% higher of cardiovascular death.What additional information would you want to know in order to make better-informed decisions regarding Avandia? 7.17.Given a normal distribution with u=100 and Q=10,if you select a sample of n=25,what is the probability X is (a)less than 95? (b)between 95 and 97.5? ©above 102.2? (d)There is a 65% chance that X is above what value? 7.21. The diameter of a brand of ping-pong ball is approximately normally distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inch. If you select a random sample of 16 ping-pong balls, (a) What is the sampling distribution of the mean? (b) What is the probability that the sample mean is less than 1.28 inches? ©what is the probability that the sample mean is between 1.31 and1.33 inches? (d) The probability is 60% that the sample mean is between will be between what two values, symmetrically distributed around the population mean? 7.27. In a random sample of 64 people, 48 are classified as “successful.” (a) Determine the sample proportion, P, of “successful” people. (b)If the population proportion is 0.07, determine the standard error of the proportion. 8.27. In a start of the twenty-first century saw many corporate scandals and many individuals lost faith in business.In a 2007 poll conducted by new York city-based Edelman public relations firm,57% of respondents say they trust business to “do what is right.”This percentage was the highest in the annual survey since 2001 (a) construct a 95% confidence interval estimate of the population proportion of individuals who trust the business to”do what is right”assuming that the poll surveyed: 1.100 individuals. 2.200 individuals. 3.300 individuals. (b) Discuss the effect that sample size on the width of confidence intervals. (c)Interprete the interval in (a) 8.32.If you want to be 95% confident of estimating the population mean to within a sampling error of +/_5 and the standard deviation is measured to be 15,what sample size is required? 8.44.In 2005,34% of workers reported that their jobs were more difficult,with more stress,and 37% reported that they worry about retiring comfortably.consider a follow-up study to be conducted in the near future. (a)What sample size is needed to estimate the population proportion of workers who reported that their jobs were more stress,to within +/- 0.02 with 95% confidence? (b)How many workers need to be sampled in order to estimate the population proportion of workers who worried about retiring comfortably to within +/- 0.02 with 95% confidence? (c )compare the results of(a) and (b).Explain why these results differ. (d)If you were to design the follow-up study,would you use one sample and ask the respondents both questions,or would you select two separate samples?Explain the rationale behind your decision. 9.1.For Ho:u=100,H1:u not equal 100,and for a sample of size n,why beta larger if the actual value of u(mean)is 90 than if the actual value of u is 75? 9.2.If you use a 0.05 level of significance in a(two-tail)hypothesis test,what will you decide if Zstat=+2.21? 9.3.If you use a 0.01 level of significance in a(two-tail)hypothesis test,what is your decision rule for rejecting a null hypothesis that the population mean is 500 if you see the Z test? 9.11.The U.S.Food and Drug Administration(FDA) is responsible for approving new drugs.Many consumer groups feel that the approval process is too easy and,therefore,too many drugs are approved that are later found to be unsafe.On the other hand,a number of industry lobbyist are pushing for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly.consider a null hypothesis that a new,unapproved drug is unsafe and an alternative hypothesis that a new,unapproved drug is safe. (a)Explain the risks of committing a type I or Type II error. (b)which type of error are the consumer groups trying to avoid?Explain. (c )which type of error are the industry lobbyists trying to avoid?Explain. (d)how would it be possible to lower the chances of both Type I and Type II errors? 9.16.if,in a sample of n=16 selected from a normal population,X bar=56 and S=12,what is the value of t STAT if you are testing the null hypothesis Ho:mean=50? 9.22.Late payment of medical claims can add to the cost of health care.An article reported that the mean time from the date of service to the date of payment for one insurance company was 41.4 days during a recent period.Suppose that a sample of 100 medical claims is selected during the latest time period.The sample mean time from the date of service to the date of payment was 39.6 days,and the sample standard deviation was 7.4 days. (a)Using the 0.05 level of significance,is there evidence that the population mean has changed from 41.4 days? (b)What is your answer in(a)if you use the 0.01 level of significance? (c )What is your answer in(a)if the sample mean is 38.2 days and the sample standard deviation is 10.7 days? (d)Because the sample size is 100,do you need to be concerned about the shape of the population distribution when conducting the t-test in( a)?Explain. 9.34. In a one-tail hypothesis test where you reject Ho only in the upper tail,what is the P-value if Z=stat=+2.00? 9.45.You are the manager of a restaurant that delivers pizza to collect dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes.A sample of 36 orders using the