Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a normal distribution with unknown population mean and known standard deviation 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for population mean is 512.00 ± 25.75." The confidence level for this interval is

And solving for the critical value we got:

Now we need to find the confidence level and for this case we can use find this probability:

And using the normal standard distribution or excel we got:

So then the confidence interval for this case is 99%

Step-by-step explanation:

For this case the random variable X is the scores for the SAT math scores and we know that the distribution for X is normal:

They select a random sample of n =100 and they construc a confidence interval for the true population mean of interest and they got:

for this problem we need know that the confidence interval for the true mean when the deviation is known is given by:

The margin of error is given by:

And the margin of error for this interval is then we can solve for the critical value in order to find the confidence level:

And solving for the critical value we got:

Now we need to find the confidence level and for this case we can use find this probability:

And using the normal standard distribution or excel we got:

So then the confidence interval for this case is 99%

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.