Suppose the age of people in a certain population are distributed normally with a mean of 37.5 years and standard deviation of 6.2 years. What is the probability of randomly selecting a person who is over 45 years old given that they are older than 40.

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 age of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability:

We can begin finding using the z score formula given by:

Using this formula we have:

And using the complement rule and the normal standard table or excel we have this:

Now we can find using the z score formula given by:

Using this formula we have:

And using the complement rule and the normal standard table or excel we have this:

And replacing into our original probability we got:

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.

1. a^4+8a^3+24a^2+32a+16

2.y^8+8y^7+28y^6+56y^5+70y^4+56y^3+28y^2+8y+1

3.x^6-3x^4y^2+3x^2y^4-y^6