Question

The time it takes for a ferry to reach a summer resort from the mainland is Normally distributed with mean 2 hours and standard deviation 12 minutes.

What should be the advertised duration of the trip (in minutes) if the ferry management does not want to be late on more than 5% of the trips but would like to minimize the advertised duration?

Answer 1

• Here X is the random variable denoting the advertised duration of the trip.
• therefore X follows normal distribution with mean 2hours i.e 120 mins and wiht standard deviation 12 minutes.
• X~Normal(120,12)
• Here we have to find the duration of the trip so that does not want to be late on more than 5% of the trip
• P(Z<)=0.05
• i.e=1.645 (i.e the z value associated with the p value)
• =1.645
• therefore X=139.74
• Hence 139.74 is the advertised duration of the trips if the ferry management does not want to be late on more than 5% of the trips.