Asupermarket has determined that daily demand for milk containers has an approximate bell shaped distribution, with a mean of 55 containers and a standard deviation of six containers. how often can we expect between 49 and 61 containers to be sold in a day?

or 68.26%.

Step-by-step explanation:

The daily demand for milk containers has a Normal (or Gaussian) distribution, and we can use values from the cumulative distribution function and z-scores to solve the question.

We know from the question that the mean of the distribution is:

And a standard deviation of:

The z-scores permit calculates the probabilities for any case whose values have a Normal o Gaussian distribution. Then, for this, we need to calculate the z-scores for 49 containers and 61 containers to establish the corresponding probabilities, as well as the differences between these two values to determine the probability between them.

These z-scores are given by:

Thus,

The z-scores for 49 and 61 containers are:

[1]

[2]

Well, this is a special case when in both cases the values are one standard deviation from the mean, but in one case () the values are smaller than the mean and in the other case () the values are greater than the mean.

In other words, the cumulative probability for (), obtained from any Table of the Normal Distribution available on the Web, is: 0.8413 (or 84.13%) and the cumulative probability for () is: 1 - 0.8413 = 0.1587 (or 15.87%), because of the symmetry of the Normal Distribution.

Then, the probability of expecting to sell between 49 and 61 containers in a day is the difference of both obtained probabilities:

or 68.26%.

See the graph below.

For a question like this, all you have to do is remember that a percentage is simply a fraction expressed as a decimal. So, all we have to do is:
, and then multiply our decimal answer by 100 to get the percentage:
= 0.34
0.34 x 100 = 34
Therefore 34% of the students walk to school.
I hope this helped and remember to please try and understand the maths that got the answer, not just writing the answer down :))