Correlation and Regression 1. Pearson's Product Moment Correlation Coefficient " [ xy - Ex Ex 2. Spearman's Rank correlation coefficient, r, = 1 - - n(n' - 1) 3. The least- squares regression line of Y against X, Y = a + bX i. b_ _xy-ExZy [xy _ 2xLy or b= - n n ii. a =y-bx or n Probability Distribution 1 . Uniform P(X = x) = _, for x = X1,X2 ,..., Xk Mean, u k +1 2 Variance, o? = K2 - 1 12 2. Binomial P(X = x)="Cop*q0-*, for x =0,1,2,.., n Mean, H = E(X) = np Variance,o' = V(X) =npq 3. Poisson P(X = x) =e*)x for x = 0,12,... x! Mean, u = E(X) = > Variance, a' = V(X) = >FORMULA LIST Sample Measurements 1. Mean, X = or fx n n 2. Median, X = Lm + 2 . C 3. Mode, * = Lma . C 4. Standard Deviation, S = Vn-1 E ( x - x) or 1 n = Vn -1 If(x - x)? or 1 in- 1 Efx _ ( [fx ) n 5. Coefficient of Variation, CV = 2 x 100 6. Mean - Mode 3 (Mean - Median) Pearson's Measure of Skewness = or Standard Deviation Standard Deviation where 1I total frequency Lm lower class boundary of a median class L mo lower class boundary of a modal class cumulative frequencies for the classes before the median class fm frequency of median class = (frequency of modal class) - (previous frequency of modal class) A 2 = (frequency of modal class) - (next frequency of modal class) class sizeQUESTION 4 a) The time it takes for a group of students to complete a Computer quiz is normally distributed with a mean of 1 hour and a standard deviation of 12 minutes. i) If a student is selected at random, what is the probability that the time to complete the quiz is at least 75 minutes? (3 marks) ii) Find the probability that the time to complete the quiz is between 50 minutes to 70 minutes. (3 marks) iii) If 65% of the students spend more than t minutes to complete the quiz, determine the value of t. (4 marks) b) A random variable Y denotes the time (in hours) it takes to complete a programming course provided by JJ Centre. The probability density function of a random variable Y is given by: f(y) =20 (12 -1), 1sys3 0, elsewhere i) Calculate the probability that it takes more than 1.5 hours to complete the course. (3 marks) i) Find the expected number of hours it takes to complete the course