A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Complete parts (a) through (c) a. What percentage of standardized test scores is between 411 and 649> % (Round to the nearest tenth as needed.) b. What percentage of standardized test scores is less than 411 or greater than 649? % (Round to the nearest tenth as needed.)c. What percentage of standardized test scores is greater dun 768? % (Round to the neatest tenth as needed.)

a)

And we can find this probability with this difference:

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

And the percentage would be 68.3%

b) For this case we can find this with the complement rule and with the result of the part a and we got:

And that represent 31.7%

c)

And we can find this probability with the complment rule like this:

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

And the percentage would be 2.3%

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".  

Part a

Let X the random variable that represent the standardized test's

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with this difference:

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

And the percentage would be 68.3%

Part b

For this case we can find this with the complement rule and with the result of the part a and we got:

And that represent 31.7%

Part c

Using the z score we got:

And we can find this probability with the complment rule like this:

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

And the percentage would be 2.3%

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.