Given f(x)=-2/3x+3 and g(x)=-2x^2-5

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

Monica [59]

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:

$\mu = 250, \sigma = 175.781$

3 0

3 years ago

mei has written 250 pages of her novel. if she is able to write at a rate of 6 pages per day for the next 30 days, how many page

Tatiana [17]

Mei will have written a total of 430 pages at the end of the 30 days.

The number of already written pages by Mei is 250.
The speed of Mei is 6 pages per day.
The total time is 30 days.
The number of pages written in 30 days by Mei is 30*6.
Mei's number of pages written in 30 days is 180.
Mei's total number of pages that she will have written at the end of 30 days is 250 + 180.
The total number of pages that Mei will have written at the end of 30 days is 430.

To learn more about speed, visit :

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#SPJ4

8 0

1 year ago

(-1/3x + 9.5) + x(3/4+2.5)

Kobotan [32]

Answer:

35x + 114

12

Step-by-step explanation:

(-1/3x + 9.5) + x(3/4 + 2.5)

(-1/3x + 95/10) + x(3/4 + 25/10)

(-x/3 + 5 × 19/2 × 5) + x(3/2² + 5²/2 × 5)

(-x/3 + 19/2) + x(3/2² + 5²⁻¹/2)

(2(-x) + 3 × 19/ 3 × 2) + x(3/2² + 5/2)

(-2x + 57/3 × 2) + x(3 + 2 × 5/2²)

-2x + 57/3 × 2 + x(3 + 2 × 5/2²)

-2x + 57/3 × 2 + x(13/2²)

-2x + 57/3 × 2 + x × 13/2²

-2x + 57/3 × 2 + 13x/2²

2(-2x + 57) + 3(13x)/3 × 2²

2(-2x + 57) + 3 × 13x/3 × 2²

2(-2x + 57) + 39x/3 × 2²

(-2 × 2x + 2 × 57) + 39x/3 × 2²

(-4x + 114) + 39x/3 × 2²

-4x + 114 + 39x/3 × 2²

-4x + 39x + 114/3 × 2²

35x + 114/3 × 2²

35x + 114/3 × 4

35x + 114/12

7 0

3 years ago

Sunrise Trail is three and a quarter miles one mile equals 5280 feet what is the length in feet of the trail

kifflom [539]

So 1 mile= 5280 feet. So first take 5280 divided by 4 (because we have a quarter mile) = 1320.
Then do 5280 x 3 (because we have three miles)= 15840 feet
then take 1320 + 15840= 17160 feet
The trail is 17,160 feet long

7 0

3 years ago

Please help In the example of the racetrack, what was the average displacement at the end of the race?

andreev551 [17]

Answer:The Indianapolis Motor Speedway is an automobile racing circuit located in Speedway, Indiana (an enclave suburb of Indianapolis) in the United States. It is the home of the Indianapolis 500 and the Verizon 200,[4] and formerly the home of the United States Grand Prix. It is the largest sports venue in the world. It is located on the corner of 16th Street and Georgetown Road, approximately six miles (10 km) west of Downtown Indianapolis.

Constructed in 1909, it is the second purpose-built, banked oval racing circuit after Brooklands and the first to be called a 'speedway'. It is the third-oldest permanent automobile race track in the world, behind Brooklands and the Milwaukee Mile. With a permanent seating capacity of 257,325,[1] it is the highest-capacity sports venue in the world.[5]

Considered relatively flat by American standards, the track is a 2.5-mile-long (4.0 km) rectangular oval with dimensions that have remained essentially unchanged since its construction. It has two 5⁄8-mile-long (1,000 m) straightaways, four geometrically identical 1⁄4-mile (400 m) turns, connected by two 1⁄8-mile (200 m) short straightaways, termed "short chutes", between turns 1 and 2, and between turns 3 and 4.

Step-by-step explanation:

5 0

2 years ago