, And Each With Its Own Boolean-Valued Outcome: A Random

As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.

Statistics provides us with very useful tools and techniques that aide us in dealing with real world scenarios. I have been able to learn several useful concepts by studying statistics that can aide me in making rational and informed decisions that are supported by the analysis results. Statistics as a discipline is the application and development of various processes put in place to gather, interpret, and analyse the information. The quantification of biological, social, and scientific phenomenons, design and analysis of experiments and surveys, and application of

• Provide at least two examples or problem situations in which statistics was used or could be used.

* We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc >

Sampling distribution of a sample statistics is the hypothetical distribution of the sample statistics of interest for a random sample, whereas the distribution of a sample is the probabilistic distribution of the ideas in the sample. The sampling distribution indicates how likely it is to get some definite sample when one draws a large amount of samples and the distribution of a sample shows how possible it is to get a particular data in a single random

Ans: the random variable is being used in statistics and probability most of the time. This is also called stochastic or aleatory variable as his has an ability of making its values vary according to the subject or according to the chance that occur. A random variable has the ability of taking a set of different kind of values that also have the different value with the value associated with it.

It is one of the most popular and well known measures of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data

Because the mean is calculated and mean is the best measure of central tendency when the data of interval or ratio scale.

In order for you to understand how I did this, I will explain that a z-score gives you a way to compare different sets of data using their standard deviations and averages. In statistics, standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to zero tells you the data points are close to the mean or average. Having a high standard deviation shows data points are spread out over a wider range of values. If x is a data point in a normal distribution, then the equation for the z-score of x is x equals x minus the average all divided by the standard deviation. Normal distribution is just a function that represents the distribution of many random variables as a symmetrical bell-shaped graph.

The normal distribution is a continuous, unimodal and symmetric distribution. For a typical normal distribution, a mesokurtic (which means to have a moderate peak and tails for a graph), definition is one that has a mean of 0 and a standard deviation of 1. While this is the case, there might be other normal distributions with means that are not 0 and a standard deviation that is not 1, for these cases, we use their means and standard deviation. For example, if a normal distribution had a mean of -2 and a standard deviation of 3, then in order to clarify that it is indeed a normal distribution, we write N(-2,3). Among the normal distributions, we have a standard normal, exponential, uniform and beta. These are varieties of distributions we can get within a normal distribution based on factors like number of cases for example and where the cases were drawn from. At times when it gets complicated to distinguish between the standard deviation of a variable and that of a sampling distribution, there is a solution. The standard deviation for a sampling distribution is called a standard error and this literally means that if a sampling distribution is normal, then 68% of its samples will lie within one standard error of the mean and 98% within 1.98 standard error of the mean. The normal distribution is useful not just due a random variable following a normal distribution, but also because the Central Limit Theorem, which is a theorem that shows the sampling distribution of the mean

A normal distribution can be regarded as the most important continuous probability distribution in statistics since it can be utilized to model several sets of measurements in business, industry, and nature. For instance, normal distributions can be used to measure the systolic blood pressure of humans, housing costs, and the lifetime of television sets through random variables. Generally, normal distributions can have any mean and positive standard deviation as the two parameters totally determine the shape of the normal curve during evaluation. In this case, the mean determines the location of the symmetry line while the standard deviation defines how much the data are spread out ("Normal Probability Distributions", n.d.).

-If both the items of interest and the items that are not of interest are least 5, the normal distribution can be used to approximate the binomial distribution.

This is a discrete random variable, where the process of obtaining the Binomial distribution is called “Bernoulli “ process. An experiment that often consists of repeated trials, each with two possible outcomes, which could be labeled as “success” or “failure”. This experiment is known as binomial experiment.

After John Graunt, many other mathematicians made contribution to the statistical studies, such as Johanm Gauss introduced normal distribution, Kal person developed standard deviation, correlation coeff, P-value Person’s chi-square test, principal component Analysis concepts, and Ronald Alymer Fisher became popular for F distribution Walter Shewhart gave control charting statistical process control. At last, Dr.

Normally distributed data – in this approach we can specify the mean and the standard deviation and data can be generated from that normal distribution. In this approach we also can give the data so that data overlaps a little.