Question

The time that is takes to traverse the Bitfrost Bridge into Asgard is normally distributed with a mean of 3.58 minutes. If 67.72% of Asgardains take longer than 3.10 minutes to cross the bridge, what is the value of the standard deviation of the times?

Answer 1

X : Time takes to to traverse the Bitfrost Bridge into Asgard

X follows normal distribution with mean = 3.58 and standard deviation

Given,

67.72% of Asgardains take longer than 3.10 minutes to cross the bridge i.e P(X>3.10) = 67.72/100 = 0.6772

P(X>3.10) = 1-P(X3.10) = 0.6772

P(X3.10) = 1-0.6772 = 0.3228

Z1 be the z-score for 3.10

Z1 = (3.10 - 3.58)/

= -0.48/Z1

P(ZZ1) = 0.3228

From standard normal tables,

P(Z-0.46) = 0.3228 ; Therefore Z1 = -0.46)

= -0.48/Z1 = - 0.48/-0.46 = 1.043478261

= 1.0435

Value of the standard deviation of the times = 1.0435