C3: Continuous Probability Distributions

Question 1

Normal Distribution

Answer 1

• derived from random phenomenon.
• widely used for continuous random variables.
• bell-shaped curve.
• assists in drawing inferences about popn parameters based on sampling.
• special frequency distribution.
• approximates other distributions.
• has 2 parameters:
(i) mu
- the mean.
- the balance point.
- curve is symmetrical about vertical line through mean.

(ii) sigma
- the standard deviation.
- controls spread of curve.

• Probability of continuous = Area under the curve
• Mean = Median = Mode
• P(of all possible outcomes) = 1
• mean = 50th percentile.

Question 2

Standard Normal Distribution

Answer 2

= occurs when mean = 0 & sd = 1 of a normal density function.
• standard normal distribution tables – used to obtain probabilities for normal distributions.

● Standardizing formula:

             Z = (X - mean) / sd

When:

• z –> 0 ___ measurement is near mean.
• +z ___ measurement is above mean.
• -z ___ measurement is below mean.

Question 3

Normal Approximation To The Binomial Distribution

Answer 3

• Conditions:

(i) n >= 30.
(ii) np >= 5 & nq >= 5.

Question 4

Normal Approximation To The Poisson Distribution

Answer 4

• Condition:

(i) lambda >= 5.