Statistics for Decision Makers - 07.02 - Normal Distributions - Calculating Probabilities

title

07.02 - Normal Distributions - Calculating Probabilities

author

Bernard Szlachta (NobleProg Ltd) bs@nobleprog.co.uk

Normal Distribution Calculator。

Online Version

http://selfstudy.nobleprog.com/normal-distribution-calculator

Download (html/javascript)

File:Normal distribution calculator.zip

Example 1。

It shows a normal distribution with

• a mean of 50
• a standard deviation of 10

The shaded area between 40 and 60 contains 68% of the distribution.

Example 2。

It shows a normal distribution with

• a mean of 100
• a standard deviation of 20

As in Example 1, the shaded area between 80 and 120 contains 68% of the distribution.

68% of the distribution is within one standard deviation of the mean.

The normal distributions shown in Example 1 and 2 are specific examples of the general rule that 68% of the area of any normal distribution is within one standard deviation of the mean.

Example 3。

It shows a normal distribution with

• a mean of 75
• a standard deviation of 10

The shaded area contains 95% of the area and extends from 55.4 to 94.6.

95% of the Area。

• For all normal distributions, 95% of the area is within 1.96 standard deviations of the mean.
• For quick approximations, it is sometimes useful to round off and use 2 rather than 1.96 as the number of standard deviations you need to extend from the mean so as to include 95% of the area.

Quiz。

Please find the quiz here

Quiz

1 A distribution has a mean of 40 and a standard deviation of 5.
Question: 68% of the distribution can be found between which two numbers?

	30 and 50
	0 and 45
	0 and 68
	35 and 45

Answer >>

35 and 45

68% of the distribution is within one standard deviation of the mean. 40 + 5 equals 45, 40 - 5 equals 35.

2 A distribution has a mean of 20 and a standard deviation of 3. Approximately 95% of the distribution can be found between which two numbers?

	17 and 23
	14 and 26
	10 and 30
	0 and 23

Answer >>

35 and 45

95% of the distribution is within 1.96 standard deviations of the mean. You can round 1.96 to 2 for an approximate answer. 20 - 2(3) equals 14, 20 + 2(3) equals 26.

3 A normal distribution has a mean of 5 and a standard deviation of 2. What proportion of the distribution is above 3?

Answer >>

0.8413

Use the "value from an area" calculator and enter a Mean of 5, a SD of 2, Above 3. You will get 0.8413.

4 A normal distribution has a mean of 120 and a variance of 100. 35% of the area is below what number?

Answer >>

116.15

Var is 100, so the SD is 10. Use the "value from an area" calculator and enter that the Mean is 120, the SD is 10, and the Shaded area is .35. Click below, and you will get 116.15.

5 A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile is placed in an advanced class. What is the cutoff score to get into the class?

Answer >>

43

Use the "Value from an area" calculator and enter a Mean of 38, a SD of 6, a Shaded area of .80. Click below, and you will get 43.05, meaning a score of 43.

6 A normal distribution of test scores has a mean of 38 and a standard deviation of 6. What percent of the students scored between 30 and 45?

Answer >>

78.7

Use the "Value from an area" calculator and enter a Mean of 38, a SD of 6, and Between 30 and 45. You will get 0.787, meaning 78.7%.

7 According to a market report about the online advertising market, spending per single customer is normally distributed with a mean of 100,000 and a standard deviation of 20,000. A company wants to target only companies spending more than 150,000 year. What percent of the market are they going to target?

	0.45%
	0.62%
	70.31%
	6.2%
	30%

Answer >>

78.7

Mean of 100,000; SD of 20,000; Above 150,000. You will get 0.0062, meaning 0.62%.