Choose all the lines that are parallel to the line pictured in the graph bellow.
1 answer:
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Answer:
A. 13.9 and 14.1 inches
See explanation below.
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".
Solution to the problem
Let X the random variable that represent the outside diameters of a population, and for this case we know the distribution for X is given by:
Where and
If we want the middle 68% of the data we need to have on the tails 16% on each one
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 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84
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
And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:
And if we solve for a we got
So the correct answer for this case would be:
A. 13.9 and 14.1 inches
Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.
Step-by-step explanation:
Linear growth :
- Population grow by a constant amount after each time period.
- The rate of change of dependent variable with respect to independent variable is a constant.
- It is represented by line on graph.
- Equation for linear growth :
, c = initial value and m is the rate of change of y with respect to x.
Exponential growth :
- Population grow by a constant ratio .
- It is represented by a curve on graph.
- Equation for exponential growth :
, a = initial value and r is rate of growth ( in decimal ) and x is time period.
Given : Jonesville's population grows by 170 people per year.
i.e .Population grow by a constant amount per year.
⇒ Jonesville is growing linearly.
The population of smithville grows by 7% per year.
i.e. Population grow by a constant ratio.
⇒Smithville is growing exponentially.
Hence, the true statement is "B. Jonesville is growing linearly and Smithville is growing exponentially."