Probability Distributions

5.2b Standard Normal Distribution Tables The characteristics of the tables of the standard normal distribution, N (0, 1) are: Case 1   P (Z > a) is the area of the shaded region in the above diagram.   Case 2 P (–∞ < Z < ∞) = 1   Case 3   P (Z > 0) = P (Z < … Read more

5.2a z–Score of a Normal Distribution   Example: (a)  A normal distribution has a mean, µ = 50 and a standard deviation σ = 10. Calculate the standard score of the value X = 35. (b)  The masses of Form 5 students of a school are normally distributed with a mean of 60 kg and a standard … Read more

5.2 Normal Distribution (A) Continuous Random Variable Continuous random variable is a variable that can take any infinite value in a certain range. (B) Normal Distribution 1.   A continuous random variable, X, is normally distributed if the graph of its probability function has the following properties.   · Its curve has a bell shape … Read more

5.1b Mean, Variance and Standard Deviation of a Binomial Distribution 2. Determine the mean, variance and standard deviation of binomial distribution. If X is a binomial discrete random variable such that   X ~ B (n, p),  then Mean of X,   μ = n p Variance of X, σ 2 = n p q Standard deviation of X, … Read more

5.1a Probability of an Event that follows a Binomial Distribution   1. For a Binomial Distribution, the probability of obtaining r numbers of successes out of n experiments is given by P ( X = r ) = c n r . p r . q n − r where P = probability X = discrete … Read more