Final Exam Review Questions Solutions Guide You will probably want to PRINT THIS so you can carefully check your answers. Be sure to ask your instructor if you have questions about any of the solutions given below. 1. Explain the difference between a population and a sample. In which of these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation. Solution: A sample is a subset of a population. A population
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Normal Distribution:- A continuous random variable X is a normal distribution with the parameters mean and variance then the probability function can be written as f(x) = - < x < ‚ - < μ < ‚ σ > 0. When σ2 = 1‚ μ = 0 is called as standard normal. Normal distribution problems and solutions – Formulas: X < μ = 0.5 – Z X > μ = 0.5 + Z X = μ = 0.5 where‚ μ = mean σ = standard deviation X = normal random variable Normal Distribution Problems and Solutions – Example
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decimal places) 2. Find the value of z if the area under a Standard Normal curve a) to the right of z is 0.3632; b) to the left of z is 0.1131; c) between 0 and z‚ with z > 0‚ is 0.4838; d) between -z and z‚ with z > 0‚ is 0.9500. Ans : a) z = + 0.35 ( find 0.5- 0.3632 = 0.1368 in the normal table) b) z = -1.21 ( find 0.5 – 0.1131 = 0.3869 in the normal table) c ) the area between 0 to z is 0.4838‚ z = 2.14 d) the area to the
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random will be between 19 and 31 is about 0.95. This area (probability) is shown fir the X values and for the z values. σ = 3 0.95 σ = 1 0.95 X 19 25 31 -2 0 +2 Normal curve showing Standard normal curve showing area between 19 and 31 area between -2 and +2 Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100
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Application of Normal mode calculations in optical spectroscopy | Phym 221 – Assignment 4 1. Introduction Normal modes are used to describe the different vibration motion in molecules. There are different types of modes for molecules in different motions and each has a certain symmetry associated with it. 2. Overview of Normal Modes Generally‚ normal modes are independent atoms in a molecule that are in motion such that they do not disturb the motion of the other molecules. Normal modes as implied
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Confirming Pages C H A P T E R 6 The Normal Distribution Objectives Outline After completing this chapter‚ you should be able to 1 2 3 Identify distributions as symmetric or skewed. 4 Find probabilities for a normally distributed variable by transforming it into a standard normal variable. Introduction 6–1 Normal Distributions Identify the properties of a normal distribution. Find the area under the standard normal distribution‚ given various z values.
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the right on block 1 with a normal force of 16 N. On a sheet of paper‚ draw the free body diagram for block 1 using the two-subscript notation from class. After completing the free body diagram‚ enter below each force and its x & y-components. Remember that the x-component is the "i" component and the y-component is the "j" component. FORCES on BLOCK 1 Weight force on block 1 by Earth W1E = 0 i + -40 j N Normal force on block 1 by Surface N1S = 0 i + 40 j N Normal force on block 1 by Hand
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Normal Distribution Normal distribution is a statistics‚ which have been widely applied of all mathematical concepts‚ among large number of statisticians. Abraham de Moivre‚ an 18th century statistician and consultant to gamblers‚ noticed that as the number of events (N) increased‚ the distribution approached‚ forming a very smooth curve. He insisted that a new discovery of a mathematical expression for this curve could lead to an easier way to find solutions to
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Table Z: Areas under the standard normal curve (negative Z) Second decimal place in z 0.06 0.05 0.04 0.03 0.09 0.08 0.07 0.02 0.01 0.0001 0.0001 0.0002 0.0002 0.00 * 0.0000 0.0001 0.0001 0.0002 0.0002 z -3.9 -3.8 -3.7 -3.6 -3.5 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0
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NORMAL DISTRIBUTION 1. Find the distribution: a. b. c. d. e. f. following probabilities‚ the random variable Z has standard normal P (0< Z < 1.43) P (0.11 < Z < 1.98) P (-0.39 < Z < 1.22) P (Z < 0.92) P (Z > -1.78) P (Z < -2.08) 2. Determine the areas under the standard normal curve between –z and +z: ♦ z = 0.5 ♦ z = 2.0 Find the two values of z in standard normal distribution so that: P(-z < Z < +z) = 0.84 3. At a university‚ the average height of 500 students of a course is 1.70 m; the standard
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