The average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed. If a single egg is randomly selected, what is the probability that the egg will be with cholesterol content greater than 220 milligrams

"The probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%)

Step-by-step explanation:

We have here a normally distributed random variable. The parameters that characterize this distribution is the mean, , and the standard deviation, .

In this question, we have that:

And we want to know the probability that a randomly selected single egg "will be with cholesterol content greater than 220 milligrams."

To answer the latter, we need to use the following key concepts:

The z-scores are standardized values and represent the distance (for the raw score) from the mean in standard deviations units. A positive z-score indicates that it is above and, conversely, a negative result that the value is below it.

The cumulative distribution function generates the values for the cumulative standard normal distribution displayed in the standard normal table.

The standard normal distribution is employed to find probabilities for any normally distributed data and we only need to calculate the corresponding z-score (or standardized value). This distribution has a and .

As we can see, all of these concepts are intertwined, and each of them is important because:

Finding the probability

We can get the z-score using the formula:

[1]

Where x is the raw value we want to standardize using the previous formula, and, in this case is 220 milligrams, milligrams.

Thus (without using units):

To consult the standard normal table, we only need , because it only has values for two decimal digits. As a result, the value will be a little inexact (but near to the true value) compared to that obtained using statistical software (or maybe a more precise table).

With this value (which is positive and, therefore, above the mean), we need to carefully see the first column of the mentioned table to find z = 0.3. Then, in the first row, we only need to select that column for which we can add the next digit, in this case, 3 (it appears as +0.03). That is, we are finding the probability for .

Then, the cumulative probability for is:

However, the question is asking for "cholesterol content greater than 220 milligrams" or

Since

Which is the same for a standardized value:

Then

Therefore

Thus, "the probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%).

The graph below shows a shaded area that corresponds to the found probability.  

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.