Question

One of the side effects of flooding a lake in northern boreal forest areas (e.g. For a hydro-electric project) is that mercury is leached from the soil, enters the food chain, and eventually contaminates the fish. The concentration in fish will vary among individual fish because of differences in eating patterns, movements around the lake, etc. Suppose that the concentrations of mercury in individual fish follows an approximate normal distribution with a mean of 0.25 ppm and a standard deviation of 0.08 ppm. Fish are safe to eat if the mercury level is below 0.30 ppm. What proportion of fish are safe to eat?

Answer 1

Answer:

$P(X$

And we can find this probability using the z score table or excel:

$P(z$

So then we can conclude that the proportion of fish that are safe to eat is about 0.734

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".  

Solution to the problem

Let X the random variable that represent the concentrations of mercury in individual fish of a population, and for this case we know the distribution for X is given by:

$X \sim N(0.25,0.08)$  

Where $\mu=0.25$ and $\sigma=0.08$

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 using the z score table or excel:

$P(z$

So then we can conclude that the proportion of fish that are safe to eat is about 0.734