The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a bell-shaped distribution, what can be said about the proportion of ratios that fall between 11.5 and 15.5

And we can find the probability with this difference

And we can use the normal standard distribution or excel and we got:

So then we expect a proportion of 0.682 between 11.5 and 13.5

Step-by-step explanation:

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

Where and

We want to find the following probability

And we can use the z score formula given by:

Using this formula we got:

And we can find the probability with this difference

And we can use the normal standard distribution or excel and we got:

So then we expect a proportion of 0.682 between 11.5 and 13.5