# Calculating Percentiles of Standard Normal Distribution

• sami23
In summary, the standard normal distribution has a mean of 0 and a standard deviation of 1. The 10th percentile of the distribution is -1.28 and the 90th percentile is 1.28. The 10th upper percentile is 0.1. The confidence interval is 90% and the area under the curve represents the population, with the mean at the center and \alpha/2 representing the shaded area in red. The 10th percentile is to the left and the 10th upper percentile is to the right.
sami23
Homework Statement
Normal: mean = 0 standard deviation = 1

Is it:
10th percentile of standard normal distribution is -1.28
10th upper percentile of standard normal distribution is 0.1
90th percentile of standard normal distribution is -1.28
10th percentile of standard normal distribution is 1.28

The attempt at a solution

Area under the curve is the Population, at the center or x is the mean, let $$\alpha$$/2 be the area shaded in red.

...lost. I know that in standard normal distribution N(mean, variance) = N(0,1) and to get the confidence interval = 1 - $$\alpha$$ = 0.1 which would be 90% (to the left)

I think it would be 10th upper percentile (to the right)

would be 0.1, 10th percentile of standard normal distribution is -1.28 and 90th percentile of standard normal distribution is 1.28? But I am not sure. Could someone please explain this to me? Thank you!

## What is the standard normal distribution?

The standard normal distribution is a probability distribution that is symmetric and bell-shaped, with a mean of 0 and a standard deviation of 1. It is often used in statistics to represent a wide range of naturally occurring phenomena.

## How is the standard normal distribution calculated?

The standard normal distribution is calculated using a mathematical formula called the standard normal density function, which is:

f(x) = (1/√(2π)) * e^(-x^2/2)

This formula takes into account the mean and standard deviation to determine the likelihood of a given value occurring.

## What is the purpose of calculating percentiles of the standard normal distribution?

Calculating percentiles of the standard normal distribution allows us to determine the likelihood of a particular value occurring within a certain range. This can be useful for making predictions and understanding the distribution of a set of data.

## How do you calculate the percentile of a given value in the standard normal distribution?

To calculate the percentile of a given value in the standard normal distribution, you can use a statistical table or a calculator that has the option to calculate cumulative probabilities. You can also use the formula P(x ≤ a) = Φ(a), where Φ(a) is the cumulative probability of the value a.

## What is the significance of the 68-95-99.7 rule in the standard normal distribution?

The 68-95-99.7 rule, also known as the empirical rule, states that approximately 68% of the values in a normal distribution will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule is often used to quickly estimate the likelihood of a value occurring within a certain range in a normal distribution.

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