A ferry carries 25 passengers. The weight of each passenger has a normal distribution with mean 168 lbs and variance 361 lb squared. Safety regulations state that, for this particular ferry, the total weight of passengers on the boat should not exceed 4250 lbs more than 5 percent of the time. What is the probability that the total weight of passengers on the ferry will exceed 4250 lbs?
The sum of normal random variables is also a normal random variable. the mean is the sum of the means and the variance is the sum of the variances. this is only true if the variables are independed, which they are in this case.
X ~ Normal( ?x = 4200 , ?x² = 9025 )
X ~ Normal( ?x = 4200 , ?x = 95 )
Find P( X > 4250 )
P( ( X – ? ) / ? > ( 4250 – 4200 ) / 95 )
= P( Z > 0.5263158 )
= P( Z < -0.5263158 )
= 0.2993344
Comment by Merlyn — June 21, 2009 @ 7:43 am