PROBLEMS FOR RELAIBILITY 1. Consider the following system: Determine the probability that the system will operate under each of these conditions: a. The system as shown. b. Each system component has a backup with a probability of .90 and a switch that is 100 percent reliable. c. Backups with .90 probability and a switch that is 99 percent reliable.Solutions 1. a. P(operate) = .92 = .81 .9 .9 .9 .9 .9 .9 .9 .9 b. [.90 + .10(.90)] [.90 + .10(.90)] = .9801 c. [.90 +
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length of labor(hrs)‚ return to work (wk)‚ number of hours working per week. 2. What statistics were used to describe the length of labor in this study? Were these appropriate? Length of labor was described in hours. No‚ because the original stratified sample of 80 had 12 people who dropped out which deviated the results. 3. What other statistic could have been used to describe the length of labor? Provide a rationale for your answer. Other statistic that could have been used to describe
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Mean‚ Median‚ Mode‚ and Range Mean‚ median‚ and mode are three kinds of "averages". There are many "averages" in statistics‚ but these are‚ I think‚ the three most common‚ and are certainly the three you are most likely to encounter in your pre-statistics courses‚ if the topic comes up at all. The "mean" is the "average" you ’re used to‚ where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median‚ your
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Mean and Standard Deviation The mean‚ indicated by μ (a lower case Greek mu)‚ is the statistician ’s jargon for the average value of a signal. It is found just as you would expect: add all of the samples together‚ and divide by N. It looks like this in mathematical form: In words‚ sum the values in the signal‚ xi‚ by letting the index‚ i‚ run from 0 to N-1. Then finish the calculation by dividing the sum by N. This is identical to the equation: μ =(x0 + x1 + x2 + ... + xN-1)/N. If you are not
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Mean‚ Mode and Median Ungrouped and Grouped Data Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data‚ along with the frequencies‚ are presented individually. Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on intervals – the range of values – being used. It is from these classes‚ are upper and lower class boundaries found. Mean Mean The ‘Mean’ is the total of all the values
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The following table gives the examination grades for 120 students. Grade Cumulative frequency 1 9 9 2 25 34 3 35 p 4 q 109 5 (a) Number of students 11 120 Find the value of (i) p; (ii) q. (4) (b) Find the mean grade. (2) (c) Write down the standard deviation. (1) (Total 7 marks) 1 2. A standard die is rolled 36 times. The results are shown in the following table. Score 2 3 4 5 6 Frequency
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involved. (c) Explain your answer to someone who has never taken a course in statistics. Solution: (a) Use the steps of hypothesis testing. Size of sample‚ n = 8 Degree of freedom = n-1 = 8-1 = 7 Sum of sample = i=1∑n=8xi = (25+27+25+23+24+25+26+25) = 200 | Time (in Hours) | Sum | Mean(xm) | (xi- xm)2 | Standard Deviation | 1 | 25 | 200 | Mean = Sum/n= 200/8= 25 | 0 | σ = √( i=1∑n=8(xi-xm)2/(n-1))= √(10/7)= √1.4285= 1.195 | 2 | 27 | | | 4 | | 3 | 25 | | | 0 | | 4 | 23 | | | 4
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Mean-Variance Analysis Mean-variance portfolio theory is based on the idea that the value of investment opportunities can be meaningfully measured in terms of mean return and variance of return. Markowitz called this approach to portfolio formation mean-variance analysis. Mean-variance analysis is based on the following assumptions: 1. All investors are risk averse; they prefer less risk to more for the same level of expected return. 2. Expected returns for all assets are known. 3. The
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Means End Chain Model Dealing with real estate purchase are considered high involvement goods that require complex decision-making. However‚ in order to understand consumers’ cognitive structures and to extract the deeper motives behind an individual behaviour in buying houses using Means end Chain model and laddering helped us to understand the why and how products are important in an individual’s life. The means end chain interview sample size was 10 and the respondents were couples‚ all aged
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Sample sizes and confidence intervals for proportions Chong Chun Wie Ext: 2768 ChongChunWie@imu.edu.my Content • Sampling distribution of sample means (SDSM) • Normality Test • Estimating a population mean: σ known • Estimating a population mean: σ unknown • Standard deviation of proportion • Confidence interval of proportion • Hypothesis testing with proportion Population and Sample Samples Populations Sampling distribution of sample means (SDSM) Sampling distribution • Example – Select
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