Question

4. The normal distribution is written as X-N(121, 162). a. State the mean value and the standard deviation. [2 marks] Mean: Standard Deviation: b. Using the normal curve below, shade the area under the range 89 < X < 137. Be sure to label the mean as well as the values for up to 3 standard deviations above and below. [2 marks] c. What percentage of data lies within the shaded region? [1 mark] 5. The entry in the standard normal table is 0.1131, what is the associated 2-score? [1 mark] 6. Using the standard normal table, determine the probability that... [4 marks) a. X<-0.11 b. X > 1.46 c. 0.15 < X < 2.00

Answer 1

u= mean then If xnN(462) and = standard deviation, for xun( 121, 16² 16 Mean 21 Standard deviation b Z- 7 us how mean If x~ N(4,02) then x-1 in Celled Standard Normal random variable. and tells many Standard the deviations from your score is. • value for Rod above the Mtot 121+16 = 137 o value for a s.d. above the lut 26 121+ 32 = o value for 3. S.d above the ll + (3) 1 mean mcan 153 meem 121f 48 169 → Similarly value for 1 sd. betow the mean • value for a s.d value for 3 s.d 121-16 = 105 181-32 = 89 K1-48 73

& shaded region. 73 89 los 4:21 137 153 169 a 137-4 P( 89-9 P( 89 cx < 137) a 1-4 =P(-22241) rusing P(-2c2co) + Ploszal) Symmetry Plocza2) + Plo<2<!) O. 4772 t 0.3413 using standard 7(89< X <137) 0.8185 Normal table 81.85 %. of Curve

© using standard Normal pl -~ < za 1.21) table 0.1131 table you can find the in book or internet) associated 2- score -1.21 -0.11-12 16 P ( X <-0.11) plz c-7.569) p(-34263) = 0.9973 outside this sange Bobability is almost zero. b 6 plx>1.46) - p(x-4) 1.464722) Plzy -7.47125) 1- Plze-7.47125) → 1-0-1 16 0.15-121 16 2 6 p(0.15 < X<2.00) <X-< {-121 il -7.5531 <za -7.4375) p(-34253) = 0.9973