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svp [43]
2 years ago
15

Grading managers. Some companies "grade on a bell curve" to compare the performance of their managers and professional workers.

This forces the use of some low performance ratings so that not all workers are listed as "above average." Ford Motor Company’s "performance management process" for this year assigned 10% A grades, 80% B grades, and 10% C grades to the company’s managers. Suppose Ford’s performance scores really are Normally distributed. This year, managers with scores less than 25 received C grades and those with scores above 475 received A grades. What are the mean and standard deviation of the scores?
Mathematics
1 answer:
Monica [59]2 years ago
3 0

Answer:

\mu = 250, \sigma = 175.781

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 grades of a population, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

For this case we have two conditions given:

P(X

P(X>475) = 0.1 or equivalently P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

So we can find a value from the normal standard distribution that accumulates 0.1 and 0.9 of the area in the left, for this case the two values are:

z= -1.28, z=-1.28

We can verify that P(Z<-1.28) =0.1[/tex] and P(Z<1.28) =0.9[/tex]

And then using the z score we have the following formulas:

-1.28 = \frac{25 -\mu}{\sigma}   (1)

1.28 = \frac{475 -\mu}{\sigma}   (2)

If we add equations (1) and (2) we got:

\frac{25 -\mu}{\sigma} + \frac{475 -\mu}{\sigma} =0

We can multiply both sides of the equation by \sigma and we got:

25+ 475 -2 \mu = 0

\mu = \frac{500}{2}= 250

And then we can find the standard deviation for example from equation (1) and we got:

\sigma = \frac{25-250}{-1.28}=175.781

So then the answer would be:

\mu = 250, \sigma = 175.781

 

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Connor is going to see a movie and is taking his 4 kids. Each movie ticket costs $13 and there are an assortment of snacks avail
EleoNora [17]

If Connor buys 3 snacks at 3 dollars each for himself and his 3 children, the net cost (including movie tickets) would be 88 dollars.

If he buys x amount of snacks, his cost will be determined by C=52+3x or C=52+3*x (both are equivalent, but not everyone knows every way to represent multiplication)

Step-by-step explanation:

To find the cost of the snacks:

Cost = Price*NumberOfSnacks, or C=p*n, or C=pn

To find the unit cost of the snack, find the price, the p value, which is 3 dollars.

Then, find the total number of snacks that will be bought. Since each person receives an equal number of snacks, 3 per person, and there are 4 people (himself and his 3 children), we can multiply 3*4 to find the n value, which is now known to be 12.

C=3*12=36. Add to the 13 dollar per person charge for tickets (52 dollars for 4 people), and you get 88 dollars.

To find the cost if he buys x amount of snacks for himself and his 3 children (assumed to be "everyone"), all costs but the n value are to be the same, creating this equation:

C=52+3x

In this context, 52 is the cost of movie tickets, 3 is the cost of the snacks, and x is the total number of snacks bought. C represents total cost.

5 0
2 years ago
Find tsa of cylinder whose height is 7cm and radios 4cm.​
ki77a [65]

Answer:

Answer

Let height =h

Total surface area=2πr(r+h)

r=7cm

⇒968=2×  

7

22

​  

×7(7+h)

⇒  

44

968

​  

=7+h

⇒h+7=22

⇒h=22−7

=15cm.

Step-by-step explanation:

6 0
3 years ago
Which of the following are solutions to 2x2 – 8x - 90? Select all that apply.
Bond [772]

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

2x^{2} -8x-90  

equate to zero

2x^{2} -8x-90=0  

so

2=-1\\b=-8\\c=-90

substitute in the formula

x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}

x=\frac{8\pm\sqrt{784}} {4}

x=\frac{8\pm28} {4}

x=\frac{8+28} {4}=9

x=\frac{8-28} {4}=-5

therefore

The solutions are x=-5, x=9

6 0
2 years ago
What is the measurement of the missing angle<br><br>​
Pie

Answer:

65

Step-by-step explanation:

115-180=65 degrees

5 0
2 years ago
Read 2 more answers
Find the solution of the system x′=−4y,y′=−2x, where primes indicate derivatives with respect to t, that satisfies the initial c
Andreas93 [3]

Answer:2y^2 = x^2+4

Step-by-step explanation:

given is a differntial equation in parametric form as

x'=-4y\\y'=-2x

We can find dy/dx by dividing y' by x'

\frac{dy}{dx} =\frac{-2x}{-4y} \\4ydy =2x dx\\2y^2 = x^2+C

(By separating the variables and integrating)

C is arbitrary constant

When x=-2, y =-2

Substitute to get

8=4+C\\C=4

So solutoin is

2y^2 = x^2+4

is the solution

5 0
3 years ago
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