Answer:
(a) 26.43%
(b) 189 seconds
Step-by-step explanation:
(a) Data
- mean: 3 minutes and 48 seconds = 3*60 + 48 = 228 s
- standard deviation, sd: 19 s
- value of interest, x: 4 minutes = 4*60 = 240 s
Z-score is calculated as follows:
z = (x - mean)/sd
z = (240 - 228)/19
z = 0.63
We want to find the next probability P(Z>0.63), which is equivalent to 1 - P(Z≤0.63)
From table, 1 - P(Z≤0.63) = 1 - 0.7357 = 0.2643 or 0.2643*100 = 26.43%
(b) We want to find z1 at which P(Z≤z1) = 0.2. From the second table, z1 is between -2.05 and -2.06.
z = (x - mean)/sd
-2.055 = (x - 228)/19
(-2.055)*19 + 228 = x
x = 189 s
