Standard Distribution

Question 1

Standard Deviation

Answer 1

• Used to measure the amount of variation in a process.
• This is one of the most common measures of variability in a data set or population
• Two Types of Equations:
  
  1. Sample
  2. Population

Question 2

What is the difference between Population and Sample?

Answer 2

• Population refers to ALL of a set
  
  • If we want to know a truth of a whole population, we use the Population equation
• Sample is a subset
  
  • We most often have a sample and are trying to infer something about the whole group.

Question 3

Use Population When:

Answer 3

1. You have the entire population
2. You have a sample of a larger population, but you are only interested in this sample and do not with to generalize your findings to the population

Question 4

Use Sample When (Most Often)

Answer 4

1. If all you have is a sample, but you wish to make a statement about the population standard deviation from which the sample is drawn, you need to use the sample standard deviation (SD)
   * Remember: It is possible to have a negative standard deviation

Question 5

How to Measure the Standard Deviation for a Sample (s)

Answer 5

Standard Deviation for a Sample (s)

1. Calculate the mean of the data set (x-bar)
2. Subtract the mean from each value in the data set
3. Square the difference found in step 2
4. Add up the squared differences found in step 3
5. Divide the total from step 4 by (n-1) for sample data
6. Take the square root of the result from step 5 to get the SD

Question 6

How to Measure the Standard Deviation for a Population (σ)

Answer 6

Standard Deviation for a Population (σ)

1. Calculate the mean of the data set (μ)
2. Subtract the mean from each value in the data set
3. Square the difference found in step 2
4. Add up the squared differences found in step 3
5. Divide the total from step 4 by N (for population data)
   
   1. (Note: At this point you have the variance of the data)
6. Take the square root of the result from step 5 to get the SD

Question 7

Standard Deviation and Variance

Answer 7

Variance is Std Dev ^2

Std Dev = Sqrt(variance)

Question 8

The Uniform Distribution

Answer 8

• The Uniform Distribution is a continuous probability distribution
• It describes the condition where all possible outcomes of a random experiment are equally likely to occur
• For the Uniform Distribution:
  
  • Probability density function f(x) is constant over the possible values of x

Question 9

The formula for Mean and Standard Deviation of Uniform Distribution

Answer 9

Question 10

Uniform Distribution Question

Answer 10

The number of mobile phones sold by Beta stores is uniformly distributed between 6 and 20 per day. Then find

• Mean
• Standard deviation
• Probability that the daily sales fall between 10 and 12
• Probability that the Beta stores will sell at least 16

Let X be the number of mobiles sold daily by beta stores, X follows the uniform distribution over (6,30). Thus the probability density function is…EXAMPLE ATTACHED

Question 11

Answer 11

Question 12

Answer 12