Question

Question 5 10 marks (a) . Suppose X is a normally distributed random variable with a mean of 15 and a standard deviation of 2.34+G Find the following probabilities. Correct your answers to 4 decimal places. (1) (ii) P(X > 14.5) P(15.3 < X < 16.8) (2 marks) (3 marks) (b) Suppose X is the sample mean of 10 observations selected randomly from a normal distribution with a mean of 15 and a standard deviation of 2.34 + ). Find the following probabilities. Correct your answers to 4 decimal places. (1) (ii) P(x < 14.8) P(14.4 < X < 15.3) (2 marks) (3 marks)

sorry R is 8

Answer 1

X NN (15, 2 X M=15, T 2.34 + B & Given R=8. (= 2.34 + 8 10 = 3:14 XNN (15, 3.14) a) (i) P(X) 14,5) = P(x - 4 x 14.5 2 14:5-15 3.14 ). - P(24-015). [2= x-47 12 0.4404 [From table z] = 0.5596 (Aus) 06. 0 0

(1) P (15.3 LX L168) 10 16-8 " 3.14 P( 153 1524 = P(0.0955 L2L0.5132) - $(0.5732) - $ (0-095s). 2 0·1157 – 0.5359 [ from 2 table] - 0.1798 (Aus) 14.8 -15 0.9929 6) XNN(MT). 0. 709 X~N(MF) here n=10, M=15, 823-14 30 0.9929 1) P(7214.8) = P ( x - 4 4 148 - 15). P(2 4-0. 2014) 01-0-20) (hum Habe) 04207 (Aus Mexani in p(14.4 Lt 2 15:3) = P( 144-15 2 2 153-15) 0.9929 0.9929 S = P(-0.604 <24 0.302) = $10:302) - $(-0.604)