Probability using mean and standard deviation excel

#PROBABILITY USING MEAN AND STANDARD DEVIATION EXCEL HOW TO#
#PROBABILITY USING MEAN AND STANDARD DEVIATION EXCEL PDF#

Most elementary courses do not cover the geometric, hypergeometric, and Poisson. Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson. Find the mean and standard deviation of X. As in (Figure), you bet that a moderate earthquake will occur in Japan during this period. On at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next 48 hours in Japan was about 1.08%. For some probability distributions, there are short-cut formulas for calculating Ој and Пѓ. Generally for probability distributions, we use a calculator or a computer to calculate Ој and Пѓ to reduce roundoff error. The standard deviation is the square root of 0.49, or Пѓ = 0.7 To find the standard deviation, add the entries in the column labeled ( x вЂ“ Ој) 2 P( x) and take the square root.

#PROBABILITY USING MEAN AND STANDARD DEVIATION EXCEL HOW TO#

To understand how to do the calculation, look at the table for the number of days per week a menвЂ™s soccer team plays soccer. To calculate the standard deviation ( Пѓ) of a probability distribution, find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root. Like data, probability distributions have standard deviations. Complete the following expected value table. If you land on blue, you donвЂ™t pay or win anything. You play each game by spinning the spinner once. The mean, Ој, of a discrete probability function is the expected value. The standard deviation of X is the square root of this sum: Пѓ = в‰€ 1.0247 For each value x, multiply the square of its deviation by its probability. The fourth column of this table will provide the values you need to calculate the standard deviation. xДЄdd the values in the third column of the table to find the expected value of X: You expect a newborn to wake its mother after midnight 2.1 times per week, on the average. Calculate the standard deviation of the variable as well. The expected value is the expected number of times per week a newborn babyвЂ™s crying wakes its mother after midnight. We say Ој = 1.1.ДЇind the expected value of the number of times a newborn babyвЂ™s crying wakes its mother after midnight. The number 1.1 is the long-term average or expected value if the menвЂ™s soccer team plays soccer week after week after week. The menвЂ™s soccer team would, on the average, expect to play soccer 1.1 days per week. The table helps you calculate the expected value or long-term average. Expected Value Table This table is called an expected value table. In this column, you will multiply each x value by its probability.

#PROBABILITY USING MEAN AND STANDARD DEVIATION EXCEL PDF#

Construct a PDF table adding a column x* P( x). To do the problem, first let the random variable X = the number of days the menвЂ™s soccer team plays soccer per week. Find the long-term average or expected value, Ој, of the number of days per week the menвЂ™s soccer team plays soccer. The probability that they play zero days is 0.2, the probability that they play one day is 0.5, and the probability that they play two days is 0.3. In other words, after conducting many trials of an experiment, you would expect this average value.ДЄ menвЂ™s soccer team plays soccer zero, one, or two days a week. This вЂњlong-term averageвЂќ is known as the mean or expected value of the experiment and is denoted by the Greek letter Ој. When evaluating the long-term results of statistical experiments, we often want to know the вЂњaverageвЂќ outcome. The Law of Large Numbers states that, as the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency approaches zero (the theoretical probability and the relative frequency get closer and closer together). In his experiment, Pearson illustrated the Law of Large Numbers.

To demonstrate this, Karl Pearson once tossed a fair coin 24,000 times! He recorded the results of each toss, obtaining heads 12,012 times. It gives information about what can be expected in the long term. As you learned in (Figure), probability does not describe the short-term results of an experiment. What is the probability that the result is heads? If you flip a coin two times, does probability tell you that these flips will result in one heads and one tail? You might toss a fair coin ten times and record nine heads. This means that over the long term of doing an experiment over and over, you would expect this average. The expected value is often referred to as the вЂњlong-termвЂќ average or mean. Mean or Expected Value and Standard Deviation

Probability using mean and standard deviation excel