The amount of natural gas that flows through a transmission line is measured in pounds of pressure. Assume that the average amount of natural gas in a 16-inch transmission main is supposed to be approximately 625 pounds per square inch. Past studies have suggested that this average varies by a standard deviation of 70 pounds per square inch. What is the probability that the Federal Energy Regulatory Commission (FERC) will randomly test a line and find the pressure to be less than 650 pounds? What is the probability that it is at most 640 pounds per square inch

a)

And we can find this probability with the normal standard table or excel:

b)

And we can find this probability with the normal standard table or excel:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the amount of gas of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with the normal standard table or excel:

Part b

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with the normal standard table or excel:

yes

step-by-step explanation:

they have to be opposite and reciprocal of eachother.