Chapter 6 Flashcards
Continuous random variables
A random variable that can take on any value contained in one or more intervals.
Very precise.
We calculate probabilities by finding the area under its probability distribution.
Area under the curve.
The probability of a single value of X is always zero.
2 properties of continuous probability distributions
- The probability that X assumes a value in any interval is between 0 and 1
- The total probability of all the intervals within which x can assume a value is 1.0
Normal distributions
When plotted, gives a bell-shaped curve that the total area under the curve is 1.0, curve is symmetric about the mean, and two tails of the curve extend indefinitely.
Each half of the bell curve has 0.5 of the probability.
Normal distribution mean
Determines where the centre of the normal distributions.
Standard deviation of normal distributions
Determines the spread of the normal distribution.
Standard normal distribution
Mean = 0
SD = 1
Z is used to denote a random variable that possesses the standard normal distribution.
Area under the curve to the left of a point
Can look up in a table.
Standardizing a normal distribution
We can convert any normal distribution into a standard normal distribution.
Z = x - u / o
Moves left to right.
How to find the corresponding x and z values when given an area under the curve.
- Find the given area in the middle of the table
- Identify the corresponding z value for the area
- converts the z to x if needed
How to convert z to x from area under standard curve
x = u + Zo
Normal approximate to binomial distribution
A normal distribution u = np, o = square root of npq can be used as a approximation to the binomial distribution when np > 5 and nq > 5
Continuity correction factor
P(x = k) subtract 0.5 from the low side and add 0.5 to the high side
P(x < k) add 0.5
P(x > k) subtract 0.5
P(a < x < b) subtract 0.5 from the low end and add 0.5 to the high side
