Use the Statistical Applet: Normal Density Curve to answer the question. Set the mean and standard deviation to 0 and 5 , respectively. Note that 0.023 of the area under the curve falls below −10.0 . Now set the mean to 10 and keep the standard deviation at 5 . Under these settings, 0.023 of the area under the curve falls below 0.0 . Proportion?

And if we solve for a we got

Step-by-step explanation:

For this case we have the initial case we have a normal distribution given :

Where and

And from the info of the problem we know that:

We can verify this using the z score formula given by:

And if we replace we got:

Now we have another situation for a new random variable X with a new distribution given by:

Where and

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.023 of the area on the left and 0.977 of the area on the right it's z=-1.995. On this case P(Z<-1.995)=0.023 and P(z>-1.995)=0.977

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

you answer is a

step-by-step explanation: