Question

2. Given a test that is normally distributed with a mean of 100 and a standard deviation of 12, find: (a) the probability that a single score drawn at random will be greater than 110 (relevant section) (b) the probability that a sample of 25 scores will have a mean greater than 105 (relevant section) (c) the probability that a sample of 64 scores will have a mean greater than 105 (relevant section) (d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105 (relevant section)

Answer 1

Date: 1 P (x>105 ) = P(Z > 3.33) = 1-PCZ43.33) from 2-table = 1- 0.9996 1o.ooo4 n=16 P(x295) or PCX >105) Let P (X<95) = P(x-4 L ANCOI) = P(Z < 95-100) Tours - 12/216 P(Z < -1.67) 1-PCR <1.67) from L-table 1-0.9525 0.0475 - IPCX <95) = P (X>105) = P(x-4 7 105-11 NYO, N O OUTS Pl > 105-100 12016 = PCZY 1.67) = 1-PCZL 1.67) from X-table al-0.9525 0.0475 01-67 09 pro b (<95) or PCX>105) - 0.0075 +0.0015 = 0.5225

o Giveno XNN(4 = 100,8:12) a) p (X>110) = P(x-4 > 110-4) EP (> 110-100) - P(X80-8333) 12 2008 1-PCZC0.8333) from z-table = 8-11-0.7967 NCORD 0.2033 0 0.83 PCX20) = 0: 2033 Ncou n=25 P(x>105) = P(x-4 2105-ef. Town of un = P(Z105-100) 12 /25 -przy 5 204 - P(ZY 2.0833) 2.08 - POZ2.0833) from Zrtable .. 1-0.9812 P(X>105) = 0.0188 10.0188 D = 64 Tel8>105) =P (x-4 ploton x 105-100 2 1/60 NCO. 0.0004 1.5 = P(Z > 3.33) 3.33