Question

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

Answer 1

Answer:

a) $P(X$

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

$P(z$

b) $P(X$

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

$P(z$

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:

$X \sim N(625,70)$  

Where $\mu=625$ and $\sigma=70$

We are interested on this probability

$P(X$

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

$z=\frac{x-\mu}{\sigma}$

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

$P(X$

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

$P(z$

Part b

$P(X$

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

$z=\frac{x-\mu}{\sigma}$

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

$P(X$

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

$P(z$