Question

What is the normal curve? How can the normal curve be used in statistics? Give a real-world example of how the normal curve may be used.

Answer 1

Normal curve is a bell-shaped or symmetrical curve which shows the probability distribution of a continuous random variable. It also represents the density curve of a normal distribution.

The total area under the normal.curve represents the sum of probabilities of all possible values of the random variable.

The area under the normal curve is 1 which is the total probability.

Also, the standard normal curve represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal distribution is mean ( μ ) and standard deviation ( σ ).

Normal curve can be used in statistics to find the probability of area under the curve or any shaded region. Most of the distributions tend to follow normal for large sample sizes, for which the probabilities can easily be found using the normal table

The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.

The standard deviation controls the spread of the distribution. A smaller standard deviation indicates that the data is tightly clustered around the mean; the normal distribution will be taller. A larger standard deviation indicates that the data is spread out around the mean; the normal distribution will be flatter and wider.

If we want to find the distribution of heights of students in a school then for large sample sizes it will tend to follow normal distribution with parameters being the average height and stand deviation of heights of atudents.