Question

The port of South Louisiana, located along 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 million tons of cargo per week (USA Today, September , ). Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of million tons.a. What is the probability that the port handles less than million tons of cargo per week (to 4 decimals)

Answer 1

a. P(X<5)=0.729

Explanation:

The question is incomplete:

"The port of South Louisiana, located along 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 0.82 million tons.

a. What is the probability that the port handles less than 5 million tons of cargo per week (to 4 decimals)."

We can solve this using the z-score.

We have a normal distribution with mean 4.5 and standard deviation 0.82.

The z-score for X=5 is:

`z=(X-\mu)/(\sigma)=(5-4.5)/(0.82)=(0.5)/(0.82)=0.6098`

Then, the probability that X<5 is:

`P(X<5)=P(z<0.6098)=0.729`