Almost all companies utilize some type of year-end performance review for their employees. human resource (hr) at a university's health science center provides guidelines for supervisors rating their subordinates. for example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. according to hr, ``if you have this tendency, consider using a normal distribution -- 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable.'' suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 20.
what is the lowest rating you should give to an ``exemplary'' employee if you follow the university's hr guidelines?
a. 76
b. 85
c. 90
d. 25

The Answer is 76.

Step-by-step explanation:

Given the normal distribution " 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable'',  we can see that exemplary employees are top 10% rated employees.

We have the formula for normal distribution:

z=(X-M)÷σ

where z is the minimum z-score for top 10% employee, X is the minimum score for top 10% employee, M is the mean of the score distribution, σ is the standard deviation of the score distribution.

The z-score we are looking for is the value "a" that separates the highest 10% from the lowest 90% i.e. P(z≤a)=0.90

If we look at z-table, corresponding value for a is 1.28155

We can now put the values in the formula:

1.28155=

So X=(1.28155×20)+50=75.631

Therefore minimum score for exemplary employee is 76.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.