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
Premium Normal distribution Standard deviation Variance
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
Premium Decimal
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. 5 Find
Premium Normal distribution Standard deviation
Whether it is by making mistakes‚ by observing others‚ or repeating a process over again‚ it is human nature to learn. In their book The Bell Curve‚ Richard Herrnstein and Charles Murray disagree and hold the position that human intelligence is inborn and measurable by IQ‚ which In turn shows how much success a single individual will have in life. The Bell Curve supports a class system‚ arguing that the intelligent are likely to become ever more dominant and prosperous‚ while the unintelligent are
Premium Intelligence quotient Intelligence
The Bell Curve The opinions of Herrnstein and Murray in their book‚ The Bell Curve is that human intelligence is both inherited and also has environmental factors that contribute to a person’s future in many different areas such as; finances‚ a career‚ when they start a family‚ and whether or not a person will break the law instead of a person’s level of education and economic status. The authors go on to say that the more intelligent people of society are keeping their distance from the less
Premium Intelligence quotient Intelligence Theory of multiple intelligences
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
Premium Normal distribution Standard deviation Probability theory
standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data 34‚ 38‚ 22‚ 21‚ 29‚ 37‚ 40‚ 41‚ 22‚ 20‚ 49‚ 47‚ 20‚ 31‚ 34‚ 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6 | | | | | 219200 48714 0197 6 This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot? 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 Solution: Weak positive linear
Premium Normal distribution Standard deviation Arithmetic mean
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
Premium Normal distribution Standard deviation
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.
Premium Normal distribution Standard deviation Variance
SECTION 2: TIME VALUE OF MONEY Decision problems in business usually involve a decision over whether to accept one alternative over another‚ or whether to implement a plan or not. In most cases‚ the effects of these decisions are felt in the future. Examples: Expand into a new market (geographical‚ consumer segment‚ etc.) or not? Now or later? Outsource production or keep it in-house? Grow organically or acquire a competitor? Or don’t grow at all? Purchase shares in Microsoft
Premium Time value of money Net present value Present value