Case Problem: Specialty Toys Specialty Toys‚ Inc.‚ sells a variety of new and innovative children’s toys. Management learned that the preholiday season is the best time to introduce a new toy‚ because many families use this time to look for new ideas for December holiday gifts. When Specialty discovers a new toy with good market potential‚ it chooses an October market entry date. In order to get toys in its stores by October‚ Specialty places one-time orders with its manufacturers in June or July
Premium Normal distribution Forecasting Prediction
Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30‚000‚ [pic] [pic] Normal distribution [pic] [pic] 2. @ 15‚000 [pic] P(stockout) = 1 - .1635 = .8365 @ 18‚000 [pic] P(stockout) = 1 - .3483 = .6517 @ 24‚000 [pic] P(stockout) = 1 - .7823 = .2177 @ 28‚000 [pic]
Premium Normal distribution
be the demand for the toy. Then X follows normal distribution with mean μ = 20000 and standard deviation σ. Then P(10000 < X < 30000) = 0.95 P( X < 20000)=0.5 P(10000 < X < 20000) = 0.475 P( X < 10000)=0.025 NORM.S.INV(0.025)=-1.96 NORM.S.INV(0.975)=1.96 Z-score of 10000 =-1.96 Z-score of 30000=1.96 σ = (30000-20000)/1.96 =10000/1.96 = 5102 Standard Deviation of 5102 The graph above shows the distribution for the demand for the Weather Teddy Bear using Specialty Toys’ forecasts based off of
Premium Standard deviation Normal distribution
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)
Premium Random variable Probability theory Cumulative distribution function
mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the 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
Premium Probability theory Binomial distribution Random variable
1. Use the sales forecaster’s predication to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. Let’s assume that the expected sales distribution is normally distributed‚ with a mean of 20‚000‚ and 95% falling within 10‚000 and 20‚000. We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So‚ we can get the standard deviation by: z = (x -
Premium Normal distribution Standard deviation
Solution to Case Problem Specialty Toys 10/24/2012 I. Introduction: The Specialty Toys Company faces a challenge of deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased‚ sales will be lost; if too many are purchased‚ profits will be reduced because of low prices realized in clearance sales. Here‚ I will help to analyze an appropriate order quantity for the company. II. Data Analysis: 1. 20‚0 00 .025 10‚0 00 30
Premium Standard deviation
The Poisson probability distribution‚ named after the French mathematician Siméon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson
Premium Random variable Probability theory
Probability Distribution Memo To: Howard Gray‚ CEO; Jean Dubois‚ VP Mechanical Watch Division; Uma Gardner‚ VP Production; Amanda Hamilton‚ VP Marketing After identifying the business problem of falling sales and an increase in rejections by the Swiss Official Chronometer Control‚ conducting a study for research will prove to identify a solution. Researchers performed a study of a sample population of 500 people. The study reveals 60% of the watches purchased are certified and the average
Premium Watch Sample size Sample
Probability Distribution Essay Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH‚ HT‚ TH‚ and TT. Now‚ let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0‚ 1‚ or 2‚ so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range‚ but are
Premium Random variable Probability theory