Standard Normal Distribution

The standard normal distribution is a probability distribution that has a mean of 0 and a standard deviation of 1. It is also known as the Z-distribution or the Gaussian distribution. The standard normal distribution is used in statistical analysis to calculate probabilities associated with a normal distribution.

Mean and Standard Deviation

The mean of a distribution is the average value of all the data points in the distribution. The standard deviation is a measure of the spread of the data points around the mean. In a normal distribution, the mean and standard deviation can be used to describe the shape of the distribution.

Options:

(a) Mean = 1 S.D =0

This option is incorrect. The mean of the standard normal distribution is 0, not 1. Additionally, the standard deviation of the standard normal distribution is 1, not 0.

(b) Mean = 1, S.D = 1

This option is not describing the standard normal distribution. A normal distribution can have any mean and standard deviation, but the standard normal distribution has a mean of 0 and a standard deviation of 1.

(C) Mean = 0, S.D =1

This option is correct. The standard normal distribution has a mean of 0 and a standard deviation of 1.

(d) Mean = 0, S.D =0

This option is incorrect. The standard deviation of the standard normal distribution is 1, not 0.

Conclusion

In conclusion, the standard normal distribution has a mean of 0 and a standard deviation of 1. Option (C) correctly describes the standard normal distribution.