A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was​ installed, the amount being spent on personal calls follows a normal distribution with an average of per month and a standard deviation of​ $50 per month. Refer to such expenses as​ PCE's (personal call​ expenses). Find the point in the distribution below which​ 2.5% of the​ PCE's fell.

Answers

Answer 1

Answer:

The point is [tex]\mu - 98[/tex], in which [tex]\mu[/tex] is the average per month.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with an average of per month and a standard deviation of​ $50 per month.

Average of [tex]\mu[/tex], standard deviation [tex]\sigma = 50[/tex]

Find the point in the distribution below which​ 2.5% of the​ PCE's fell.

This is below the 2.5th percentile, which is the X when Z has a pvalue of 0.025, so X when Z = -1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.96 = \frac{X - \mu}{50}[/tex]

[tex]X - \mu = -1.96*50[/tex]

[tex]X = \mu - 98[/tex]

The point is [tex]\mu - 98[/tex], in which [tex]\mu[/tex] is the average per month.


Related Questions

ILL GIVE BRAINLEST- select each classification that describes the triangle shown.

Answers

Answer:

Obtuse, isosceles

Step-by-step explanation:

Classify. Two same length sides make it isosceles

A larger angle than 90° make it obtuse

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

solve for x i will give brainlest

Answers

Answer:

[tex] \displaystyle x = 3.97[/tex]

Step-by-step explanation:

we are given a exponential equation

[tex] \displaystyle {3}^{x} = 78[/tex]

we want to figure out x

remember that,

[tex] \displaystyle \log_{a}( {a}^{c} ) = c[/tex]

thus

take [tex]\log_3[/tex] both sides:

[tex] \displaystyle \log_{3}( {3}^{x} ) = \log_{3}(78) [/tex]

use the formula:

[tex] \displaystyle x = \log_{3}(78) [/tex]

by using calculator

[tex] \displaystyle x = 3.97[/tex]

Devora explored a secret cave. 48\text{ m}48 m48, start text, space, m, end text from the entrance, she found an empty chest with a map drawn on it. The map showed treasure buried 95\text{ m}95 m95, start text, space, m, end text from the entrance to the cave. From the treasure, the map showed a 30\degree30°30, degree angle between the chest and the entrance, as shown below. Devora faced the entrance, then turned a certain number of degrees to her left and walked until she got to the treasure.

Answers

Answer:

82°

Step-by-step explanation:


Draw the two-dimensional shape
that makes up the faces of this
solid shape.

Answers

Answer:

like this?

Step-by-step explanation:

Which statement about this figure is true?

Answers

Answer:

We need the figure

Explanation:

Can't describe a figure with no knowledge on what is it like.

Answer:

It has no rotational symmetry

What is the volume of this

Answers

343cm^3! i looked it up lol plz mark brainpower
The anwser 21 because 7x3=21 And the volume u add the other 7 around the corners so add 4 and 7x4=28

I REALLY NEED HELP pls I didn’t study at all

Answers

Answer:

ok so the numbers are 21%, 3/20, 25.6%, 2.24, and .24 we are ordering from least to greatest

Step-by-step explanation: First we need to figure out what 3/20 is and its 0.15 so 3/20 comes first then 0.24 then 2.24 then 21% then 25.6%

what is 5.706 correct to 2d.p​

Answers

5.71 that's it! no more I hope I helped in any thing

What point is 4 points from m

Answers

Answer:

A

Step-by-step explanation:

Have a nice day :)

Answer:

point A

Step-by-step explanation:

counting m 4 steps down to A

A probability model includes p(red)=2/7 and P(blue)=3/14. Select all the probabilities that could complete the model.
Answer Key:
A: P(green)= 2/7, P(yellow)=2/7
B: P(green)=3/8, P(yellow)=1/8
C: P(green)=1/4 P(yellow)=1/4
D: P(green)= 5/21 Pyellow)= 11/21 E. P(green)= 3/7 P(yellow)=1/14

Answers

Answer:

The answer is "Option D".

Step-by-step explanation:

In this question, the shape of the model is not declared that why we assume that it has four sides in which two sides are given that is:

[tex]\to P(red)=\frac{2}{7} \\\\\to P(blue)=\frac{3}{14}[/tex]

other probabilities  are:

[tex]\to P(green)= \frac{5}{21} \\\\\to P(yellow)= \frac{11}{21}[/tex]

write the log equation as an exponential equation

Answers

Answer:

[tex](z+5)^{(3x+4)} = 9[/tex]

Step-by-step explanation:

Tip: When [tex]log_{a} b = c[/tex], [tex]a^{c} =b[/tex] is also true.

[tex]log_{z+5} (9) = 3x+4[/tex]   | Original equation

[tex](z+5)^{(3x+4)} = 9[/tex]      | Use tip

Answer:

z+5 3(x+4

This is your answer.

i will mark you brainless if you can solve this​

Answers

Answer:

1.cube

6faces

2.i can't understand it what is it but I think rectangle

3.i think it's pyramid if it is it has

5 faces

3. cone

1 face

expresa en metros
20km=​

Answers

Answer:

20000  m

Step-by-step explanation

multiplica el valor de longitud por 1000

Answer:

20000m

Step-by-step explanation:

1k = 1000

20k = 20*1000

= 20000

WILL MARK BRAINLY FOR FIRST ANSWER

Answers

Answer:

(5,-6)

Step-by-step explanation:

On a map, the distance between Los Angeles, CA and San Francisco, CA is 51.5 cm. What is the actual distance if the map scale is 1 cm:8 mi.?
A) 4 mi
B) 4.12 mi
C) 41.2 mi
D) 412 mi

Answers

Answer:

it's D) (412 mi) trust me

Step-by-step explanation

The actual distance if the map scale is 1 cm:8 mi is 412 meters.

We have given that,

On a map, the distance between Los Angeles, CA and San Francisco, CA is 51.5 cm.

We have to determine

The actual distance if the map scale is 1 cm:8 mi.

What is the actual distance?

Distance is a numerical measurement of how far apart objects or points are. In physics or everyday usage, the distance may refer to a physical length or an estimation based on other criteria.

Therefore the total distance is 412 meters.

To learn more about the distance visit:

https://brainly.com/question/2854969

#SPJ2

grand pa gave $35 to linda and diane. linda received $19. find the ratio of the amount of money linda received to the amount of money diane received

Answers

I don’t know about this question and I’ve answered plenty before just not this one

Simplify each expression using order of operations to reveal a fact about Earth Day. Earth Day is observed in this many countries... 6 + 2 18 + 200 – 8 x 10 2 e е​

Answers

Answer:

YOOOOOOOOSHI :33

Step-by-step explanation:

Help

See the picture

Answers

Answer:

it's 4

Step-by-step explanation:

it's 4 because you times

I NEED HELP FAST> THIS PROBLEM IS SO CONFUSING!! the ^ mean exponents
after simplifying, what will x be equivalent to? (a^4)^6=a^x

Answers

Answer:

x will be equivalent to 24

Step-by-step explanation:

apply the multiplication rule to the exponents in (a^4)^6

4 times 6= 24, so (a^4)^6 is equivalent to a^24

What are some advantages of different ways to solve an equation?

Answers

Answer:

When you have different forms of equations you can then see equivalencies.  the different forms of equations can then be solved, each in its own manner.  meaning sometimes you can not solve one way because the equation is nested within another, a function in a function. F(x)=f(g(x))  Then you can work the problem around to different forms until you get your solution

7. Lines that intersect forming a square corner is called
a. Parallel lines b. Intersecting lines c. Perpendicular lines

Answers

Answer:

c. Perpendicular lines

Step-by-step explanation:

Anthony is going to invest in an account paying an interest rate of 2%
compounded monthly. How much would Anthony need to invest, to
the nearest cent, for the value of the account to reach $15,000 in 10
years?

Answers

Answer:

12283.01

Step-by-step explanation:

PLZ ANSWER I WILL MAKE YOU THE BRAINLIEST NO FAKE LINKS

Answers

Answer:

b. At Field Day,...

Step-by-step explanation:

In order to solve for the answer to the problem, one would have to calculate 1/2 divided by 5. So, b. is your answer.

I would appreciate Brainliest, but no worries.

Hannah worked 26 of the math problem for the math competition. Van worked 35 of the math problem. How many math problem did they work together​

Answers

61

26 + 35 = 61
Not sure if this is what your looking for but hope it helps
0 Because they both were in a competition with each other

Given that v = (5,-4,4) and w = (9,-2,7) evaluate v • w.
A. 81
B. 19
C. (45,8,28)
D. (-40,-16,-8)

Answers

Answer:

81

Step-by-step explanation:

Evaluating v • w

Recall: Given vectors a and B in Cartesian plane, x, y and z

vector a = [ax ay az] and b = [bx by bz]

The dot product is :

a•b = axbx + ayby + azbz

Using the relation above,

v • w = (5*9) + (-4*-2) + (4*7)

v • w = 45 + 8 + 28

v • w = 81

Hence, v • w = 81

I NEED HELP PLZ ( WILL GIVE BRAINLYIST) ( NO LINKS)

Answers

9514 1404 393

Answer:

  66 cm²

Step-by-step explanation:

The area of the polygon is the sum of the areas of the triangle and the rectangle it sits on. The dimensions of the triangle can be found by examining the top/bottom dimensions shown and the left/right dimensions shown.

The width (base) of the triangle is the difference between the lengths of the bottom and top horizontal lines: (12 -9) cm = 3 cm.

The height of the triangle is the difference between the lengths of the left and right sides of the figure: (9 -5) cm = 4 cm.

The dimensions of the rectangle are shown a the bottom and the left sides of the figure.

  triangle area = 1/2bh = 1/2(3 cm)(4 cm) = 6 cm²

  rectangle area = LW = (12 cm)(5 cm) = 60 cm²

Total polygon area = 6 cm² + 60 cm² = 66 cm²

Could I get some help with this app

Answers

Answer:

you but question you don't understand and some one will help you with it can take a bit though

Step-by-step explanation:

The zeroes of the function are

Answers

Answer:

NO Help without knowing what the function is.

Where is it?

Step-by-step explanation:

Answer:

The x-intercepts

Step-by-step explanation:

where the line crosses the x-axis (could be once or mulitple times.) Find by taking the function, solving it until you have 1 or multiple binommials (they should be in parenthesis), and then making them equal to one. For example i would write x - 2 = 0 which would end up being x = 2. The coordinate would be (2,0).

Hope this helps!

-2 is the ________ of 2

Answers

Answer: -2 is the numerical opposite of the number 2. Any numbers opposite is it's negative form. (except for 0 due to there being no opposite for something that is not negative or positive.)

Diego decided to paint his bedroom walls. His room is 12 feet long 11 feet wide, and 9 feet tall.how many square feet will Diego be painting

Answers

Answer:

396

Step-by-step explanation:

if his walls are 11 feet wide and 9 feet tall multiply 11 times 9 which equals 99 times for which equals 396

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