Question

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest bulk cargo port in the world. The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week.† Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of 0.88 million tons.

a) What is the probability that the port handles less than 5 million tons of cargo per week? (Round your answer to four decimal places.)

b) What is the probability that the port handles 3 or more million tons of cargo per week? (Round your answer to four decimal places.)

c) What is the probability that the port handles between 3 million and 4 million tons of cargo per week? (Round your answer to four decimal places.)

d)

Assume that 86% of the time the port can handle the weekly cargo volume without extending operating hours. What is the number of tons of cargo per week that will require the port to extend its operating hours? (Round your answer to one decimal places.) ________ tons of cargo per week

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	4.5
std deviation   =σ=	0.8800

probability that the port handles less than 5 million tons of cargo per week :

probability =

P(X<5)

=

P(Z<0.57)=

0.7157

b)

probability that the port handles 3 or more million tons of cargo per week :

probability =

P(X>3)

=

P(Z>-1.7)=

1-P(Z<-1.7)=

1-0.0446=

0.9554

c)

probability =

P(3<X<4)

=

P(-1.7<Z<-0.57)=

0.2843-0.0446=

0.2397

d)

for 86th percentile critical value of z=		1.08
therefore corresponding value=mean+z*std deviation=			5.5 Tons