## What is the percentage rule for normal distribution?

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 is the normal distribution table?

The standard normal distribution table is a compilation of areas from the standard normal distribution, more commonly known as a bell curve, which provides the area of the region located under the bell curve and to the left of a given z-score to represent probabilities of occurrence in a given population.

How do you read Z table for normal distribution?

To use the z-score table, start on the left side of the table go down to 1.0 and now at the top of the table, go to 0.00 (this corresponds to the value of 1.0 + . 00 = 1.00). The value in the table is . 8413 which is the probability.

How do you explain the 68 95 and 99.7 rule?

What is the 68 95 99.7 rule?

1. About 68% of values fall within one standard deviation of the mean.
2. About 95% of the values fall within two standard deviations from the mean.
3. Almost all of the values—about 99.7%—fall within three standard deviations from the mean.

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

Apply the empirical rule formula:

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

### How do you find the 75th percentile with mean and standard deviation?

This can be found by using a z table and finding the z associated with 0.75. The value of z is 0.674. Thus, one must be . 674 standard deviations above the mean to be in the 75th percentile.

What is the z value for 95%?

-1.96
The critical z-score values when using a 95 percent confidence level are -1.96 and +1.96 standard deviations.

Is z-score a percentage?

A z-score table shows the percentage of values (usually a decimal figure) to the left of a given z-score on a standard normal distribution.

## How is the 68% of a distribution determined?

68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean (μ).

## When to use the 68 95 and 99.7 rule?

The 68-95-99 rule It says: 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviation of the mean. 99.7% of the population is within 3 standard deviation of the mean.

What is 68 95 99.7 rule and how do you explain the 68 95 99.7 rule of normal distribution in math terms?

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

How many standard deviations is 75% of the mean?

two standard deviations
At least 75% of the data will be within two standard deviations of the mean. At least 89% of the data will be within three standard deviations of the mean. Data beyond two standard deviations away from the mean is considered “unusual” data.

### How do you find the 75th percentile?

Example 1: Arrange the numbers in ascending order and give the rank ranging from 1 to the lowest to 4 to the highest. Use the formula: 3=P100(4)3=P2575=P. Therefore, the score 30 has the 75 th percentile.

### How do you convert percentage to percentile?

Steps of Percentile Formula

1. Step 1: Arrange the data set in ascending order.
2. Step 2: Count the number of values in the data set and represent it as r.
3. Step 3: Calculate the value of q/100.
4. Step 4: Multiply q percent by r.
5. Step 5: If the answer is not a whole number then rounding the number is required.

What is the Z for 90%?

1.645
Confidence Intervals

Desired Confidence Interval Z Score
90% 95% 99% 1.645 1.96 2.576

Why is Z 1.96 at 95 confidence?

The approximate value of this number is 1.96, meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean. Because of the central limit theorem, this number is used in the construction of approximate 95% confidence intervals.

## How do you convert z-score to percentage?

Subtract the value you just derived from 100 to calculate the percentage of values in your data set which are below the value you converted to a Z-score. In the example, you would calculate 100 minus 0.22 and conclude that 99.78 percent of students scored below 2,000.