a) A manager of a computer store knows that 19% of PC sold out returned to his store for repair within one year. Five of these PCs, whose characteristic can be assumed to be independent of each other, are sold out. (i) What is the probability that at most two of these PCs have returned for repair? (ii) Find the mean number of PCs returned for repair and also find its variance.
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- he Princeton Review, a company that tracks information about various colleges, reports that 30% of CofC students are out-of-state students. If we took many samples of CofC students, and for each sample calculate the proportion $\hat{p}$ of out-of-state students in that sample, what would be the center of this distribution?9.An automobile insurer has found that repair claims are Normally distributed with a mean of $530 and a standard deviation of $480. (a) Find the probability that a single claim, chosen at random, will be less than $490. (b) Now suppose that the next 60 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average X¯ of the 60 claims is smaller than $490. (c) If a sample larger than 60 claims is considered, there would be __________ chance of getting a sample with an average smaller then $490. (NOTE: Write ''LESS'', ''MORE'' or ''AN EQUAL''.)The shape of the mean-variance frontier that results from the combination of a riskless and arisky asset is…..:a. Is U-shaped, tilted 90 degrees clockwise.b. Is a straight line passing from the mean-variance points of the two assets.c. Is a hyperbola.d. Consists of two straight lines, each connecting one of the two assets to a risk-freeportfolio
- Give an explanation why this statement is either true or false: Portfolio contains n assets. Therefore, portfolio variance for this portfolio is the function of 2n covariances and n variances.A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 25 adult Americans and asks them whether or not support the proposed changes . To say that the distribution of the sample proportion of adults who respond yes, is approximately normal , how many more adult Americans does the researcher need to sample in the following cases? (a) 15% of all adult Americans support the changes (b) 20% of all adult Americans support the changesA stock analyst wondered whether the mean rate of return of financial, energy and utility stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the following table (in percents): Financial Energy Utilities 10.76 12.72 11.88 15.05 13.91 5.86 17.01 6.43 13.46 5.07 11.19 9.90 19.50 18.79 3.95 8.16 20.73 3.44 10.38 9.60 7.11 6.75 17.40 15.70 Source: Morningstar.com Required: (a) State the null and alternative hypothesis. (b) Are the mean rates of return different at the alpha = 0.05 level of significance? Please explain your answer, citing numeric and other evidence in support of your response.
- The accompanying data are x = advertising share and y = market share for a particular brand of soft drink during 10 randomly selected years. x 0.104 0.072 0.072 0.077 0.086 0.047 0.060 0.050 0.070 0.052 y 0.137 0.127 0.120 0.086 0.079 0.076 0.065 0.059 0.051 0.039 b)Calculate the equation of the estimated regression line. (Round your answers to four decimal places.) d)Calculate a point estimate of ?e. (Round your answer to five decimal places.)The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 17% while that of the latter is only 12%. If tips are normally distributed with a standard deviation of 9%. what is the probability that in a random sample of 13 tips recorded from waiters and waitresses who introduce themselves and 13 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter? Probability =A recent Gallup Poll interviewed a random sample of 1523 adults. Of these, 868 bought a lottery tickets in the past year. Suppose that in fact (unknown to Gallup) exactly 60% of all adults bought a lottery ticket in the past year. If Gallup took many simple random samples of 1,523 people, the sample proportion who bought a ticket would vary from sample to sample. The sampling distribution would be close to normal with a mean of 0.6 and a standard deviation of___ A)0.4899 B)0.0251 C)0.00016 D)0.0126
- The student will conduct a test of a single variance. Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. A sample standard deviation of 15 minutes is the same as a sample variance of ["", ""] minutes. find the a. Degrees of freedom = ["", ""] b. Chi2 test statistic = ["", ""] c. p-value =Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed. a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days. b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below. 4641056443743774 SAMPLE MEAN =? SAMPLE STANDARD DEVIATION =? c. Using the results of part (b), determine what type of test is…A supervisor at a local widget making company has been monitoring the output of one of the machines used to manufacture small aluminum plates. Past data indicate that if the machine is operating "properly," the length of the plates produced by this machine can be modeled as being normally distributed with a mean of 117 centimeters and a standard deviation of 5.2 centimeters. Suppose 16 plates produced by this machine are randomly selected. What is the probability that the average length of these 16 plates will be between 116 and 120 centimeters when the machine is operating "properly?" Z and t TABLES ARE GIVEN AS QUESTIONS 28-29. PLEASE SHOW ALL YOUR CALCULATIONS.CORRECT ANSWER WITHOUT CALCULATIONS WILL BE AWARDED PARTIAL CREDIT. Paragraph В I
