order to make the most appropriate recommendation to Management‚ a Managerial report has been prepared that addresses following issues: 1. Normal Probability Distribution sketch used to approximate the demand distribution with the its mean and Standard Deviation 0.4750 0.4750 0.95 10‚000 20‚000 30‚000 10‚000 20‚000 30‚000 Figure 1: Normal Probability Distribution Curve for Expected demand Expected Demand = 20‚000 Hence‚ Mean () = 20‚000 The probability of demand units
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Chapter 9 Monte Carlo methods 183 184 CHAPTER 9. MONTE CARLO METHODS Monte Carlo means using random numbers in scientific computing. More precisely‚ it means using random numbers as a tool to compute something that is not random. For example1 ‚ let X be a random variable and write its expected value as A = E[X]. If we can generate X1 ‚ . . . ‚ Xn ‚ n independent random variables with the same distribution‚ then we can make the approximation A ≈ An = 1 n n Xk . k=1
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visual acuity is sharpest at the fovea and decreases with increasing angle of eccentricity (Cowey & Rolls‚ 1974). This has been attributed to factors such as a decline in cone density and an increased receptive field size (Millodot et al.‚ 1975). Normal measures of visual acuity as a function of retinal eccentricity can be best described in reference to results obtained by Millodot et al. (1975) who plotted the minimum angle of resolution (MAR) as a function of target distance from fixation (eccentricity)
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Math 221 Quiz Review for Weeks 5 and 6 1. Find the area under the standard normal curve between z = 1.6 and z = 2.6. First we look for the area of both by doing “2nd ‚Vars‚ NORMALCDF” and inputting “-1000‚ “Z‚” 0‚ 1 then find the difference between both. 2. A business wants to estimate the true mean annual income of its customers. It randomly samples 220 of its customers. The mean annual income was $61‚400 with a standard deviation of $2‚200. Find a 95% confidence interval for the true mean
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deviation--”average” difference between the mean of a sample and each data value in the sample 14+ 2.51 = Mean of 14 and SD of 2.51 Distribution Shape • Normal • Skewed • Multimodial NORMAL CURVE • Mean is the focal point from which all assumptions made • Area under curve = 100% • Total area divided into segments (these %’s are always the same in the normal curve) – Between Mean & One SD = 68.26% – Between Mean & Two SD = 95.45% – Between Mean & Three SD = 99.7% Distribution Shape Skewed • Most scores
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have knowledge of unauthorized aid on this or [assignment‚ quiz‚ paper‚ test]. 2 Pg 212 #14) A normal population has a mean of 12.2 and a standard deviation of 2.5. A) Compute the z value associated with 14.3. - z = (14.3 – 12.2)/2.5 z value is .84 B) What proportion of the population is between 12.2 and 14.3? - Looking for .84 on the curve
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statistical test(s) to answer this question. * These histogram are clearly asymmetrical and the superimposed normal curve is a little bit do not fit to them well‚ infact the histogram are skewed to the right so the sample is non-normal distribution * The sample mean is far above the median. Other important measures of the normality are the skewness and kurtosis. (In normal distribution the values of skew and kurtosis are close to 0). However in this sample‚ both of them are large positive
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Inferential Statistics • Descriptive statistics (mainly for samples) • Our objective is to make a statement with reference to a parameter describing a population • Inferential statistics does this using a two-part process: • (1) Estimation (of a population parameter) • (2) Hypothesis testing Inferential Statistics • Estimation (of a population parameter) - The estimation part of the process calculates an estimate of the parameter from our sample (called a statistic)‚ as a kind of “guess” as to
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Summary Chapter 1-7 Chapter 1 * Population – consists of members of a group which you want to draw a conclusion * Sample – portion of population * Parameter – numerical measure that describes a characteristic of a population * Statistic – numerical measure that describes a characteristic of a sample * Descriptive statistics – collecting‚ summarizing and presenting data e.g. survey * Inferential statistics – drawing conclusions about a population based on sample data
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nice to be able to do the same for means. Just as we did before‚ we will base both our confidence interval and our hypothesis test on the sampling distribution model. The Central Limit Theorem told us that the sampling distribution model for means is Normal s with mean μ and standard deviation SD ( y ) = n Copyright © 2010 Pearson Education‚ Inc. Slide 23 - 3 Getting Started (cont.) n n All we need is a random sample of quantitative data. And the true population standard deviation‚
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