Normal Distribution Homework Solutions

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Students studying statistics probable know or have heard about normal distribution. Also called the Gaussian distribution, such probability distribution has symmetry about the mean of the data. At, you can get normal distribution homework solutions from expert online tutors. We can help you get a better grasp of the topic so you can solve problems on your own.

The need for normal distribution

Probability distributions like Poisson distribution and binomial distribution are useful only for discrete variables. This means they are relevant only distinct events occurring. In case of mathematical distributions that deal with quantities with continuously varying magnitude, continuous distribution is required. The best theoretical distribution for this is normal probability distribution.

Normal distribution is used for displaying several statistical data regarding economic and business problems. The continuous variables are governed by the law of normal model. In statistics, the normal model is one of the most crucial probability models. As a student, you must be well adept to the topic. Getting online help with normal distribution assignment solutions is one of the best ways of learning more about the topic.

What is normal distribution?

Also called bell curve, normal distribution naturally occurs in several situations. For instance, the bell curve shows relevance in a lot of competitive exams. Most of the students tend to score the average marks, while relatively smaller group score the highest or lowest marks. Such distribution created has resemblance with that of a bell. Symmetrical nature of the bell curve means half the data is on either side of the mean.

Such a pattern of distribution is followed by many groups. You should know exactly when to use normal distribution assignment solutions. It is used widely in statistics, business and even by government bodies. Some examples of normal distribution include:

  • Salaries
  • People’s heights
  • Blood pressure
  • Measurement errors
  • IQ scores

Normal distribution and binomial distribution

Normal distributions can be considered to be an approximation to binomial distributions. Binomial distributions have a tendency of forming continuous curve when the sample size is large enough. If the probabilities of outcomes in a binomial distribution are nearly equal, there is a close correspondence with the curve. In fact, this is true even for small sample size. When working on normal distribution homework solutions, you should have a clear distinction between normal and binomial distribution.

The Empirical Rule

For normal distributions, there is an empirical rule. This rule states that almost all the data shall fall within three standard deviations of mean. It also specifies the percentage of data falling within those standard deviations. It can be broken down into three parts:

  • The first standard deviation from mean contains 68% of the data
  • Within 2 standard deviations, 95% of the data is there
  • 99.7% of data are within 3 standard deviations.

This rule is also known as the Three Sigma Rule or 68-95-99.7 Rule.

Normal distribution properties

Before you start working on normal distribution homework solutions, you should know its basic properties. They are:

  • Mean, median and mode of the distribution are equal
  • The distribution curve is symmetric around mean, i.e., at the centre
  • Exactly 50% of the values are to right of the centre, with other 50% being to the left.
  • The area under curve is one.

Standard deviation of normal distribution

The distribution’s spread is controlled by the standard deviation. Small standard deviation is an indication of tight clustering of data around mean. This means a taller normal distribution. On the other hand, large standard deviation signifies data being spread out around the mean. In this case, the normal distribution is wider and flatter. The normal distribution assignment solutions you get from us include the necessary calculation of standard deviation.

Distribution of data in standard normal model

The normal distribution having standard deviation of 1 and mean of 1 is known as standard normal model. To get an idea of the distribution of data in this model, the data can be plotted in graph. In case of even distribution of data, bell curve can be used. This curve has majority of points on inner part, with a small percentage on the tails of the curve.

You can ask for normal distribution homework solutions from to get a better idea about the data distribution. In case of standard normal model around 5% of data falls into the tails, with around 90% in between. The examination scores of students can be an example of such normal distribution. Around 2.5% students get very low and 2.5% get very high. The rest don’t get excessively high or low scores.

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