Question

Answer all please number 2

Answer 1

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