an office manager purchased 39 boxes of pens for the staff. each box contains 6 black pens and 4 blacks pens. Use the distribute
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Answer:
D. The center remains constant, and the area in the tails of the distribution decreases.
Step-by-step explanation:
Hello!
Be it two independent random variables, X~N(μ;σ²) and U~Xₙ², the variable t is determined by the quotient between a random variable N(0;1) and the square root of a Chi-Square variable divided by its degrees of freedom:
As a consequence of this, the structure of the distribution depends on the parameter n (degrees of freedom), it is centered in zero and has a bell-shape similar to the normal distribution.
It has a mean and variance:
E(t)= 0 for n > 1
V(t)= n > 2
As you can see the variance of the distribution is directly affected by its degrees of freedom, which means that when the degrees of freedom change, the variance of the distribution change and so does its shape.
When ↑n ⇒ ↑V(t) ⇒ The area under the tails increases.
When ↓n ⇒ ↓V(t) ⇒ The area under the tails decreases.
In this example, the degrees of freedom of the distribution decreased from 40 to 20, then the variance of the distribution decreases and it "flattens", i.e. the area under the tails gets lowered.
The E(t) isn't affected by the modification of n, so the distribution remains centered in zero.
I hope this helps!
Answer:
Percent change = 5.4%
Step-by-step explanation:
Given:
Number of students voted last year = 762
Number of students voted this year = 721
Change in the number of students who voted from last year to this year is given by the difference of their number. This gives,
Change in the number of students that voted = 762 - 721 = 41
Now, percentage change in the number of students that voted is given as:
Therefore, the percent change in the number of students that voted is 5.4%.