What Is Normal Probability Distribution With Example

Around 997 of values are within 6 standard deviations of the mean. Around 95 of values are within 4 standard deviations of the mean.

Normal Probability Distribution

A random variable x whose distribution has the shape of a normal curve is called a normal random variable.

What is normal probability distribution with example. What is the probability density function of the normal distribution. The mean m and the standard deviation s. Most of the people in a specific population are of average height.

The normal probability distribution is very common in the field of statistics. For example the height of all people of a particular race the length of all dogs of a particular breed iq memory and reading skills of people in a general population and income distribution in an economy all approximately follow the normal probability distribution shaped like a bell curve. The normal distribution is described by two parameters.

We write x nm s 2. Around 68 of values are within 2 standard deviations of the mean. The empirical rule or the 68 95 997 rule tells you where most of your values lie in a normal distribution.

Height of the population is the example of normal distribution. And standard deviation 20 mm. Distribution of blood pressure distribution of blood pressure can be approximated as a normal distribution with mean 85 mm.

The following diagram shows the formula for normal distribution. The number of people taller and shorter than the average height people is almost equal and a very small number of people are either extremely tall or extremely short. For example to find the cumulative probability of a z score equal to 121 comparing the row of the table holding 12 with the column holding 001the table shows that the probability that a standard normal random variable will be less than 121 is 01131ie.

The data follows a normal distribution with a mean score m of 1150 and a standard deviation sd of 150you want to find the probability that sat scores in your sample exceed 1380. Is pz 121 01131. Scroll down the page for more examples and solutions on using the normal distribution.

Finding a z score you collect sat scores from students in a new test preparation course. Whenever you measure things like peoples height weight salary opinions or votes the graph of the results is very often a normal curve.

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