solve k = 20.275 d) P ( 17 < X < 21) P ( (17 -18)/2.5 < Z < ( 21-18)/2.5) P ( -0.4 < Z < 1.2) = 0.8849 – 0.3446 = 0.5403 ( 4 decimal places) 4. In a sample of 25 observations from a Normal Distribution with mean 98.6 and standard deviation 17.2‚ find: Ans: a) n = 25‚ [pic] = ( = 98.6‚ [pic] = /n = 17.2/(25 = 3.44 [pic]( N
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The Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business‚ number of customers in waiting lines‚ number of defects in a given surface area‚ airplane arrivals‚ or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies‚ e.g.‚ to model the number of prairie dogs found in a square mile of prairie. The major difference between Poisson and Binomial
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Mathematics): Survival distributions Age-at-death random variable T0 – age-at-death (lifetime for newborn) random variable To completely determine the distribution of T0 ‚ we may use (for t ≥ 0)‚ (1) (cumulative) distribution function: F0 (t) = Pr(T0 ≤ t) (2) survival function: s0 (t) = 1 − F0 (t) = Pr(T0 > t) (3) probability density function: f0 (t) = F0 (t) = (4) force of mortality: µ0 (t) = d F0 (t) dt f0 (t) −s0 (t) = 1 − F0 (t) s0 (t) Requirements: (1) For distribution function‚
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expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is ‚ formally defined by Variance - The variance of a discrete random variable X measures the spread‚ or variability‚ of the distribution‚ and is defined by The standard deviation is the square root of the variance. Expectation - The expected value (or mean) of X‚ where X is a discrete random variable‚ is a weighted average of the possible values that X can take‚ each value
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A population of measurements is approximately normally distributed with mean of 25 and a variance of 9. Find the probability that a measurement selected at random will be between 19 and 31. Solution: The values 19 and 31 must be transformed into the corresponding z values and then the area between the two z values found. Using the transformation formula from X to z (where µ = 25 and σ √9 = 3)‚ we have z19 = (19 – 25) / 3 = -2 and z31 = (31 - 25) / 3 = +2 From the area between z =±2 is 2(0
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1-1 Kiddie Land Gym Overview of the case: Starting in March Kiddie Land would begin to promote a new a new product Super Gym Outdoor children’s Exercise center. The problem or the issue was the company has never shipped something this big‚ they had to come up with ideas of how to make a profit and how to reach it to the customers. Case Questions: 1. Advantages and disadvantages of purchasing a two-wheeled trailer for each store to use for delivery of the Super Gym • Advantage
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Probability distribution Definition with example: The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable‚ i.e. what is the possible number of times that head might occur? It is 0 (head never occurs)‚ 1 (head occurs once out of 2 tosses)
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Normal Distribution It is important because of Central Limit Theorem (CTL)‚ the CTL said that Sum up a lot of i.i.d random variables the shape of the distribution will looks like Normal. Normal P.D.F Now we want to find c This integral has been proved that it cannot have close form solution. However‚ someone gives an idea that looks stupid but actually very brilliant by multiply two of them. reminds the function of circle which we can replace them to polar coordinate Thus Mean
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Channels of Distribution In the uncertain fluctuating market of today‚ it is essential for a company to hold on and face those uncertainties in order to survive. Consumers can be an aid for a company’s survival‚ thereby it is essential for consumers to get the goods of a company whenever and however they need them. Here is where distribution channels come in and give hand. "Channels of distribution are the different paths that goods passed through in moving from the producer to the consumer"‚ (Meyer
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Is Wealth Distribution Today Just? In current times we often observe that many members of our society receive less than other members regardless of whether they are no less deserving. In contrast‚ there are some who have ownership over assets and earn income that they may not be deserving of. The distributive balance is upset and wealth distribution today can thus be seen as a social injustice. This injustice that is becoming more noticeable as people start to become aware of the facts‚ as we can
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