Table of Contents

- 1 How do you find the percentage of a mean and standard deviation?
- 2 How many percent of the cases fall between and +2sd in the normal curve?
- 3 What percentage of the area falls above the mean?
- 4 How do you find the 68 95 and 99.7 rule?
- 5 What percent of the data lie between 1 standard deviation below the mean and 2 standard deviation above the mean?
- 6 What percentage of scores lies between the mean and 1 standard deviation for a normal distribution with a mean of 100 and a standard deviation of 15?
- 7 What percentage of the data falls below the mean?
- 8 How many percent of the data are lying 3 standard deviations above the mean?
- 9 What is the standard deviation of the distribution on the left?
- 10 What is the standard score of the distribution on the right?
- 11 How do you find the z-score of a standard normal distribution?

## How do you find the percentage of a mean and standard deviation?

To find this type of percent deviation, subtract the known value from the mean, divide the result by the known value and multiply by 100.

## How many percent of the cases fall between and +2sd in the normal curve?

Regardless of what a normal distribution looks like or how big or small the standard deviation is, approximately 68 percent of the observations (or 68 percent of the area under the curve) will always fall within two standard deviations (one above and one below) of the mean.

**What percentage of the area falls below mean of a normal distribution?**

For normal distribution, approximately 68\% of the area will fall within two standard deviations of the mean. So, for both above the mean and below the mean, 68\% of the area falls between.

### What percentage of the area falls above the mean?

The percentage of scores will fall above the mean value in a normal curve is 50\%.

### How do you find the 68 95 and 99.7 rule?

Apply the empirical rule formula:

- 68\% of data falls within 1 standard deviation from the mean – that means between μ – σ and μ + σ .
- 95\% of data falls within 2 standard deviations from the mean – between μ – 2σ and μ + 2σ .
- 99.7\% of data falls within 3 standard deviations from the mean – between μ – 3σ and μ + 3σ .

**How do you find the mean and standard deviation?**

To calculate the standard deviation of those numbers:

- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result.
- Then work out the mean of those squared differences.
- Take the square root of that and we are done!

## What percent of the data lie between 1 standard deviation below the mean and 2 standard deviation above the mean?

The Empirical Rule. You have already learned that 68\% of the data in a normal distribution lies within 1 standard deviation of the mean, 95\% of the data lies within 2 standard deviations of the mean, and 99.7\% of the data lies within 3 standard deviations of the mean.

## What percentage of scores lies between the mean and 1 standard deviation for a normal distribution with a mean of 100 and a standard deviation of 15?

This rule tells us that around 68\% of the data will fall within one standard deviation of the mean; around 95\% will fall within two standard deviations of the mean; and 99.7\% will fall within three standard deviations of the mean.

**What percentage of the area falls within 1 standard deviation above and below the mean?**

68\%

The Empirical Rule or 68-95-99.7\% Rule can give us a good starting point. This rule tells us that around 68\% of the data will fall within one standard deviation of the mean; around 95\% will fall within two standard deviations of the mean; and 99.7\% will fall within three standard deviations of the mean.

### What percentage of the data falls below the mean?

The Empirical Rule states that 99.7\% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68\% of the data falls within one standard deviation, 95\% percent within two standard deviations, and 99.7\% within three standard deviations from the mean.

### How many percent of the data are lying 3 standard deviations above the mean?

99.7\%

The Empirical Rule states that 99.7\% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68\% of the data falls within one standard deviation, 95\% percent within two standard deviations, and 99.7\% within three standard deviations from the mean.

**What percentage of scores in a normal distribution is between +1 and 1 standard deviation of the mean?**

In a normal curve, the percentage of scores which fall between -1 and +1 standard deviations (SD) is 68\%.

## What is the standard deviation of the distribution on the left?

The distribution on the left is a normal distribution with a mean of 48 and a standard deviation of 5. The distribution on the right is a standard normal distribution with a standard score of z = −0.60 indicated.

## What is the standard score of the distribution on the right?

The distribution on the right is a standard normal distribution with a standard score of z = −0.60 indicated. Z-scores measure the distance of any data point from the mean in units of standard deviations and are useful because they allow us to compare the relative positions of data values in different samples.

**What is 95\% of the mean with a standard deviation?**

95\% is 2 standard deviations either side of the mean (a total of 4 standard deviations) so: And this is the result: It is good to know the standard deviation, because we can say that any value is: likely to be within 1 standard deviation (68 out of 100 should be)

### How do you find the z-score of a standard normal distribution?

Example. Using a standard normal table “backwards,” we first look through the body of the table to find an area closest to 0.025. The z -score corresponding to a left-tail area of 0.025 is z = −1.96. Now, therefore, the upper z -score will be z = 1.96, by the symmetry property of the standard normal distribution.