Chapter 8: Probability Distributions Flashcards
What is a probability distribution?
A list of all the possible outcomes together with their expected probabilities
Example: Flipping a fair coin results in two outcomes with equal probabilities
What are the two possible outcomes in a binomial distribution?
Success and Failure
Examples: Flipping a coin (Heads or Tails), Rolling a die (6 or not 6)
How is a binomial distribution denoted?
B(n, p) where n=number of trials and p=probability of success
What are the conditions for a binomial distribution?
- Fixed number of trials (n)
- Each trial has 2 outcomes (success p or failure q)
- Trials are independent
- Probability of success is constant
What is the formula to find probabilities using the binomial distribution?
(p + q)^n
What does the term ‘nCr’ on a calculator represent?
N=number of trials and r=number of successes
What is the mean (expected value) of a binomial distribution B(n, p)?
np
What is a normal distribution?
A smooth, bell-shaped curve that is a common model for real-life situations
What is the notation for a normal distribution?
N(μ, σ²) where μ=mean and σ²=variance
What are the conditions for a normal distribution?
- Data is continuous
- Distribution is symmetrical
- Mode, median, and mean are approximately equal
What percentage of data values lie within 1 standard deviation of the mean in a normal distribution?
Approximately 68%
What percentage of data values lie within 2 standard deviations of the mean in a normal distribution?
Approximately 95%
What percentage of data values lie within 3 standard deviations of the mean in a normal distribution?
Approximately 99.8%
What does a standardised score indicate?
How many standard deviations away from the mean the data values are
How is a standardised score calculated?
(Score - Mean) / Standard Deviation
What does a positive standardised score indicate?
The value is above the mean
What does a negative standardised score indicate?
The value is below the mean
What does a standardised score of zero indicate?
The value is equal to the mean
What is the purpose of quality assurance?
To ensure products are all of the same quality and standard
What is involved in the process of quality assurance?
Checking samples to ensure they are as close as possible to the target value
What is the purpose of checking samples in quality assurance?
To ensure products are all of the same quality and standard
It involves selecting samples that are close to the target value for consistent quality.
What is the sampling technique used for in quality assurance?
To take regular samples and calculate sample mean, median, and range
The specific technique may vary by manufacturer.
What are control charts used for?
To plot sample values and see how far they are from the expected value
This helps determine if the manufacturing process is functioning correctly.
What does a Control Chart consist of?
5 lines: Target Value, Upper Warning Line, Lower Warning Line, Upper Action Limit, Lower Action Limit
These lines help monitor the quality of the manufacturing process.
What is the Target Value in a Control Chart?
The middle line where sample values should be close to
It represents the desired quality level.
What do the Upper and Lower Warning Lines represent?
2 SD above and below the target value
2SD corresponds to 95%, meaning only 5% of samples should fall outside these lines.
What action is taken if a sample average is plotted above or below the warning line?
Another sample is taken and checked for problems
Production may be stopped if issues are detected.
What do the Upper and Lower Action Limits indicate?
3 SD above and below the target value
Almost all sample averages should fall within these limits.
What happens if a sample average is outside the Action Limits?
Production is stopped immediately and machinery is reset
This is a critical action to ensure quality control.
