Use the Normal model N(98,15) for the IQs of sample participants. What IQ represents the 17th percentile? Use the appropriate Excel function to calculate your answer and round to one decimal place.

=NORM.INV(0.17,98,15)

Step-by-step explanation:

Consider X represents the IQs of sample participants.

Then X follows the Normal Distribution with mean 98 and standard deviation 15.

That is,

The probability value is 17th percentile (that is 0.17)

To find the value of X using Excel, the Inverse Normal Distribution is used.

The Excel function =NORM.INV(0.22,105,17) is used to find the IQs of sample participants.

The rules for change of coordinates are:

r = √(x^2 + y^2)

θ = tan(y/x)

and:

x = r*cos(θ)

y = r*sin(θ)

1) Now we have the equation:

r = (9/7)*cos(θ) + 2*sin(θ)

Let's multiply both sides by r:

r^2 = r*(  (9/7)*cos(θ) + 2*sin(θ) )

r^2 = (9/7)*r*cos(θ) + 2*r*sin(θ)

Now we can replace:

r*cos(θ) by x and r*sin(θ) by y

r^2 = (9/7)*x + 2*y

And we know that:

r = √(x^2 + y^2)

then:

r^2 = x^2 + y^2

So we can replace that in our equation:

x^2 + y^2 = (9/7)*x + 2*y

This is the equation in cartesian coordinates.

2) Now we want to describe the curve.

We can rewrite this as:

[x^2  - (9/7)*x] + [ y^2 - 2*y] = 0

Now we can complete squares:

So we need to add and subtract:

(4.5/7)^2 and 1^2

[x^2  - 2*(4.5/7)*x + (4.5/7)^2 -  (4.5/7)^2] + [ y^2 - 2*y + 1 - 1]  = 0

(x - (4.5/7) )^2 + (y - 1)^2   - 1 - (4.5/7) = 0

(x - (4.5/7) )^2 + (y - 1)^2  = 1 + 4.5/7

So this is the equation of a circle, centered at:

( 4.5/7, 1) and with a radius √(1 + 4.5/7)