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Answer:
Population Mean = 2.0
Population Standard deviation = 0.03
Step-by-step explanation:
We are given that the inspector selects simple random samples of 30 finished products and computes the sample mean product weight.
Also, test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds.
Now, mean of the population is given the average of two extreme boundaries because mean lies exactly in the middle of the distribution.
So, Mean, =
= 2.0
Therefore, mean for the population of products produced with this process is 2.
Since, we are given that 5% of the values are under 1.9 pounds so we will calculate the z score value corresponding to a probability of 5% i.e.
z = -1.6449 {from z % table}
We know that z formula is given by ;
~ N(0,1)
-1.6449 = ⇒
⇒ 0.0608 *
{as sample size is given 30}
⇒ = 0.03 .
Therefore, Standard deviation for the population of products produced with this process is 0.0333.
A circle with center and radius
has equation
If we substitute in this equation, we have
This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:
The expression simplifies to
The solutions to the associated equation are
So, the parabola is negative between the two solutions: