Question

Your Turn Open the normal table (opens in a new window) and use it to answer the following questions. 1. As the Z-scores go up in value, from -3.49 to 3.49, what do you notice about the about the areas? The areas get smaller • * as the z-scores increase. 2. What is the area to the left of z = 0? Area 0.50 3. If the total area under the curve is equal to 1, what is the area to the right of 2 = 0? Area = 0.50 x (Click to view hint) 4. What is the area to the left of 2 = -0.25? Area = 0.40 5. What is the probability that z is less than -0.25? P(Z <-0.25) = 0.40 x (Click to view hint) 6. What is the area to the right of 2 = -0.25? Area 0.60 * (Click to view hint) 7. What is the probability that z is greater than -0.25? P(Z > -0.25) = 0.60 * (Click to view hint) 8. What is the probability that is less than 0.62? P(Z < 0.62) = 0.73 x (Click to view hint) MacBook Air F2 F4 FO FZ 98 A 2 $ 4 3 % 5 & 7 6 8 9

Answer 1

Note: It is to be noted that as per question I have given Answers using the Z-score cummulative left table:

  
Answer :- 1. Let when us to understand try - graphically what happens the given z. scores go up in valuu (say from 3.49 to 4). -3.49 Z=0 3.49 40 Z:0 4.0 P[ -3.49<7 5 3.49] P[-4.0 < < <4.07 00 Z-score we Hence, the area will increase value go up. Quantitatively can calculate - P[ -349 $ 253.49] P[ Z $ 3.49] - P[ 25-3.49] 0 999 52 PL-40 SZ $4.0] PL Z=4.0] - PLZ & -4.0) 0.99994 Answer etic about wymmetric 2. since the standard normal distribution is Z-0. Hence, PL z 20] - P[zzo] Also, PL - SZ 3) = 1 { Arian under the normal probability curen] P[ 220 ] + P[ zso) = 1

= P[220] + P[ z 20] 2 P[ z 20) P[220] I using symmetricity of stand - -ard Normal curve about z=0 o} 1/2 = 0.5 0.5 =0.5 Answer Hence, P[ zzo] =P[ zso] Aria to the left of 7-0 =0.5. Z=0 ® [230] 3. 3. Aria to the the right of Z=0. 0.5 PL 220] -0.5. Answer Z=0 Z 20 4. Aria to the left of Z= -0.25 PL Z 3-0.25) = Answer 0.401294 5. P[Z< -0.25] = 0:401294 Answere 6. -0.25 Z=0 Area to the right of 2 = -0-25. PLZ > -0.253° = 1 P[ Z <0·25] = 0.59 8 706 Answer 7. Plz7-0.25 = 0.590706 Answer