Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 60% of the recent graduates annual salary exceeds $40000. Suppose you take a simple random sample of 51 recent graduates. Note: round all z scores to decimal places and all other numbers to 4 decimal places. Find the probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that there is a 0.9279 = 92.79% probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000.

Normal Probability Distribution

In a normal distribution 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]

It 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, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that:

60% of the recent graduates annual salary exceeds $40000, hence p = 0.6.A sample of 51 is taken, hence n = 51.

The mean and the standard error are given by:

[tex]\mu = p = 0.6[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.6(0.4)}{51}} = 0.0686[/tex]

The probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000 is the p-value of Z when X = 0.7, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.7 - 0.6}{0.0686}[/tex]

[tex]Z = 1.46[/tex]

[tex]Z = 1.46[/tex] has a p-value of 0.9279.

0.9279 = 92.79% probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000.

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Related Questions

What is the perimeter of a square with a side length of 7 cm?


A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Answers

Answer:

D. 28 cm

Step-by-step explanation:

P=4s

P=4(7)

P=28

Answer:

D. 28cm

Step-by-step explanation:

P = 4s

P = 4(7cm)

P = 28cm

=> D. 28cm

HELP ASAP PLEASE
NO LINKS

A computer was purchased at a sale at a discount of 15%. If $688.50 was paid for it,
and this price includes 8% sales tax, then what was the original price without tax or
discount?

Answers

Based on the discount rate and the sales tax, the original price of the computer was $750.

What was the original price?

First find the price before tax. This can be found as:

= Computer price / (1 + tax)

= 688.50 / (1 + 8%)

= $637.50

Then find the price without the discount as:

= Price without tax / (1 - discount rate)

= 637.50 / (1 - 15%)

= $750

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5-2x > 3x-10

Solve the inequality

Answers

Answer:x<3 that shout be right. I calculated it.

Step-by-step explanation:

Simplify the following.
-
1. 3m - 2n + 5m
2. -b - b + 5
3. 50 - 9 - 8C + 5
-

Answers

Answer:

1.[tex]8m-2n[/tex]
2.[tex]-2b+5[/tex]
3.[tex]-8c+46[/tex]

Step-by-step explanation:

Given the following questions:

[tex]3m-2n+5m[/tex]
[tex]-b-b+5[/tex]
[tex]50-9-8c+5[/tex]

To simplify the following we are going to have to regroup and combine like terms which means we are going to use inverse of operations on terms with similar variables.

Question one:
[tex]3m-2n+5m[/tex]
[tex]3m-2n+5m=3m+5m-2n[/tex]
[tex]3m+5m-2n[/tex]
[tex]3m+5m=8m[/tex]
[tex]=8m-2n[/tex]

Question two:
[tex]-b-b+5[/tex]
[tex]-b-b=-b+-b=-2b[/tex]
[tex]=-2b+5[/tex]

Question three:
[tex]50-9-8c+5[/tex]
[tex]50-9-8c+5=-8c+50-9+5[/tex]
[tex]-8c+50-9+5[/tex]
[tex]50-9=41[/tex]
[tex]-8c+41+5[/tex]
[tex]41+5=46[/tex]
[tex]=-8c+46[/tex]

Which means your answers are "8m - 2n, -2b + 5, and -8c + 46."

Hope this helps.

Can someone do this for me

Answers

Answer:

A - 10 feet

D - 5 seconds

Step-by-step explanation:

Insert 12 for r the radius and 1500 for V the volume.

12 = [tex]\sqrt{}\frac{3(1500)}{\pi h}[/tex]

Square both sides

144 = [tex]\frac{4500}{\pi h}[/tex]

Solve 144 = [tex]\frac{4500}{\pi h}[/tex]: h = [tex]\frac{125}{4\pi }[/tex]

h = [tex]\frac{125}{4\pi }[/tex] or 9.9 rounded to the nearest foot,

h = 10

t = [tex]\sqrt\frac{2(200)}{16}[/tex]

t = [tex]\sqrt\frac{400}{16} = 25[/tex]

t = [tex]\sqrt{5^{2} }[/tex]

t = 5

The temperature in some region of Alaska equals 13 F. Convert this temperature to Celsius

Answers

Answer:

10.5* Celsius

Step-by-step explanation:

Its easy to do, this is the right answer

please help me please

Answers

Answer:

2/3

Step-by-step explanation:

Looking at the graph, it looks like the line goes through (6,10) and (-6,-8). We can "subtract" the points like so:

(6-(-6))/(10-(-8))

=12/18

=2/3

You can remember this trick as "rise over run".

I hope this solution helped you. Happy mathing!

What is the value of x? (Please hurry)​

Answers

Answer:

8 root 2 or 11.3

Step-by-step explanation:

square 16 and divide by two to find square of other sides. Then root it to find answer

Answer:   8 root 2 or 11.3

Step-by-step explanation:

square 16 and divide by two to find square of other sides. Then root it to find answer

5.5x = 11? Please help. :c

Answers

Answer:

The value x would equal to 2
11 divided by 5.5 = 2
5.5 x 2 =11



Step-by-step explanation:

Have a great rest of your day
#TheWizzer

You need the x to be alone so to do that you divide both sides by 5.5 which gives you

x = 2

Cora watched 30 movies for a combined total of 55 hours over her last summer break. Some of the movies were 1.5 hours long, and others were 2.5 hours long.
How many of Cora's movies were 2.5 hours long?

Answers

The number of movies that are 2.5 hours long that Cora watched is 10 hours.

What are the linear equations that represent this question?

a + b = 30 equation 1

1.5a + 2.5b = 55 equation 2

Where:

a = movies that are 1.5 hours long

b = movies that are 2.5 hours long

How many movies are 2.5 hours long?

Multiply  equation 1 by 1.5

1.5a + 1.5b = 45  equation 3

Subtract equation 3 from 2

1b = 10 hours

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Steve bought 24 ounces of his favorite cereal. He put equal amounts of the cereal in 4 containers. How many ounces did he put in each container?​

Answers

The answer is
24 devidid by 4 is 6

Donetta is investing $6000 in a stock fund that is offering a constant annual interest of 5%

Answers

make me brainliest to the bones.

Derek and his friends drove from San Francisco to Lake Tahoe to go skiing. The average speed that they traveled during each leg of the trip is shown on the map. They drove 30 min in the city, 3 h on the highway, and 30 min up the mountain.
Write a piecewise function to represent the distance that Derek traveled during his four hour trip.

Answers

The piecewise function of the travel of the car is now described in detail:

[tex]x (t) = 30\cdot t,\,0 \le t < 0.5[/tex]  

[tex]x(t) = 15 + 60\cdot (t-0.5)[/tex],  [tex]0.5\le t < 3.5[/tex]  

[tex]x(t) = 195 + 45\cdot (t-3.5)[/tex],  [tex]3.5\le t \le 4[/tex]  

How to build a piecewise function

A piecewise function is a group of functions working on certain intervals, which corresponds to three expressions in this case. Likewise, the car moves at constant speed and the resulting distance is equal to the sum of initial position ([tex]x_{o}[/tex]), in miles, and the product of speed (v), in miles per hour, and time (t), in hours.

Then, the piecewise function of the travel of the car is now described in detail:

[tex]x (t) = 30\cdot t,\,0 \le t < 0.5[/tex]   (1)

[tex]x(t) = 15 + 60\cdot (t-0.5)[/tex],  [tex]0.5\le t < 3.5[/tex]   (2)

[tex]x(t) = 195 + 45\cdot (t-3.5)[/tex],  [tex]3.5\le t \le 4[/tex]    (3)

Remark

The map with key information of velocities is missing. We proceed to show the required information:

City - 30 miles per hour

Highway - 60 miles per hour

Mountain - 45 miles per hour

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Chloe is installing new windows in her house and needs to determine the amount of sealant she will need around the outside edge of each rectangular window. Each of the windows has an area of 2,160 Inches squared with a length of 60 inches. What is the perimeter of each window?

To find the width of each window, use the formula w = StartFraction A Over l EndFraction, where w represents the width, A represents the area, and l represents the length. To find the perimeter, use the formula P = 2 l + 2 w, where P represents the perimeter, l represents the length, and w represents the width.

Answers

Answer:

240

Step-by-step explanation:

because each side is 60 inches so do 60x4 and you get 240

Answer:

Option D!

Step-by-step explanation:

Hope this helps.

25 pts
A rectangular storage box is 12 in.
wide, 15 in. long, and 9 in. high. How
many square inches of colored paper
are needed to cover the surface of
the box?

Answers

Answer:

1,620

Step-by-step explanation:

L x W x H

L = 15

W = 12

H = 9

15 x 12 = 180

180 x 9 = 1620

Which expression is equivalent to 173. 1710 ?
A 173+10
th

6 173-10
© 173.10
O
1710

Answers

Answer:

option C

Step-by-step explanation:

hope this help u

find the area of a square if its side length is:
Part A. 1/5 cm
Part B. 3/7 units
Part C. 11/8 inches
Part D. 0.1 meters
Part E. 3.5 cm

Answers

The area of each given square is:

Part A: 1/4 cm²

Part B: 9/47 units²

Part C: 1.89 inches²

Part D: 0.01 meters²

Part E: 12.25 cm²

What is the Area of a Square?

Area of a square, with side length, s, is: A = s².

Part A:

s = 1/2 cm

Area = (1/2)² = 1/4 cm²

Part B:

s = 3/7 units

Area = (3/7)² = 9/47 units²

Part C:

s = 11/8 inches

Area = (11/8)² = 1.89 inches²

Part D:

s = 0.1 meters

Area = (0.1)² = 0.01 meters²

Part E:

s = 3.5 cm

Area = (3.5)² = 12.25 cm²

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Your friend operates a business and has the following demand curve. Complete the table, and use the information provided to find your friend’s profit-maximizing price and level of output

Answers

A demand curve shows the quantity demanded of a product at each price.

What is a demand curve?

Your information is incomplete as the table isn't given. Therefore, an overview will be given.

A demand curve simply means a graphical representation of the relationship between price and quantity demanded.

In this case, a demand curve shows the quantity demanded of a product at each price. The profit maximizing price is when the marginal cost equals marginal revenue.

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The profit-maximizing price is when the marginal cost equals marginal revenue.

An individual’s utility-maximizing choices can lead to a demand curve.

What is the demand curve?

Demand can be defined as the total amount of goods or services that consumers are willing and able to purchase at a given price.

In Economics, there are primarily two (2) factors that affect the availability and the price at which goods and services are sold or provided, these are demand and supply.

The marginal decision rule—generally produce downward-sloping demand curves.

This section shows how an individual’s utility-maximizing choices can lead to a demand curve.

Hence, The profit-maximizing price is when the marginal cost equals marginal revenue.

Learn more about the demand curve on:

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#SPJ4

Find the quotient of 2. 5 × 10-3 and 7. 1 × 106. What can be concluded about the solution? Check all that apply. The E indicates that the solution is given in scientific notation. The coefficient is 3. 5211. The exponent is 10. The solution can be written in scientific notation as 3. 5211 × 10-10. The solution is 35,211,000,000.

Answers

Scientific notation is the way through which a very small or a very large number can be written in shorthand. The quotient of 2.5×10⁻³ by 7.1×10⁷ is 3.5211×10⁻¹¹.

What are Scientific notations?

Scientific notation is the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

We know we need to divide 2.5×10⁻³ by 7.1×10⁷. Therefore, if we divide the two numbers the solution will be,

[tex]\dfrac{2.5 \times 10^{-3}}{7.1 \times 10^7}\\\\ = \dfrac{2.5}{7.1} \times 10^{-3-7}\\\\= 0.35211 \times 10^{-10}\\\\= 3.5211 \times 10^{-11}[/tex]

Hence, the quotient of 2.5×10⁻³ by 7.1×10⁷ is 3.5211×10⁻¹¹.

Learn more about Scientific notation:

https://brainly.com/question/1740231

Answer:

A. The E indicates that the solution is given in scientific notation.

B. The coefficient is 3.5211.

D. The solution can be written in scientific notation as 3.5211 × 10^-10

Step-by-step explanation:

Edge 2023

What is the approximate
volume of this cylinder? (radius is 3 cm and the height is 12 cm)

a. 36 cm3
b. 339 cm3
c. 226 cm3 1
d. 324 cm3


Answers

Answer:

a.36 cm³

Step-by-step explanation:

Explanation:- because 3 ×12 =36 so ans is 36cm³..

hope helps u

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between the penguins and the stingrays? StartFraction 81 Over 7 EndFraction feet 28 feet 45 feet 63 feet.

Answers

The distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

What is proportional segment between parallel lines?

In two triangle in which the one side of the first triangle is parallel to the one side of the other triangle, two similar triangle formed.

Due to this similar triangle the segment formed by the parallel line are proportional segment.

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays.

The map of the zoo is attached below.

The distance from whale to shark is 18 ft, and this side is parallel to the path from the penguins to the stingrays. Suppose the distance between the penguins and the stingrays is x meters.

Thus, in the given triangle, the ratio of these two sides will be equal to the ratio of their corresponding sides. Hence,

[tex]\dfrac{x}{18}=\dfrac{42}{27}\\x=\dfrac{42}{27}\times18\\x=28\rm\; ft[/tex]

Thus, the distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

Learn more about the similar triangle here;

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Answer:

28

Step-by-step explanation:

Did on edge 2022

After eating at a restaurant, Mr. Jackson’s bill before tax is $42.50 The sales tax rate is 8%. Mr. Jackson decides to leave a 20% tip for the waiter based on the pre-tax amount. Part A. How much is the tax?

Answers

Answer:

$3.40

Step-by-step explanation:

Look at image above...

Damian owns a small business selling bagels. he knows that in the last week 40 customers paid cash, 66 customers used a debit card, and 18 customers used a credit card.
if next week, he is expecting 300 customers, about how many would you expect to pay with cash? round your answer to the nearest whole number.

Answers

Ddg went to space he is the first rapper to go to space

Write the following as an inequality.
8 is greater than or equal to w, and w is greater than 4 use w only once in your inequality

Answers

Answer:

8 ≥ w > 4

Step-by-step explanation:

This says the w is greater or equal to 8 but it also says that w is greater than 4.

Answer:

8 ≥ w > 4

Step-by-step explanation:

Because 8 is greater than or equal to w, and w is greater than 4.

PLS HELPpppppppppppp ;0

Answers

Answer:

reflection

Step-by-step explanation:

by examination

Answer:

A reflection off the x axis

Step-by-step explanation:

Hope this helps!!!

If Jonah’s lunch cost $27.50, and he paid $1.65 sales tax. What is the percent of sales tax?

Answers

Answer:

6.38%

Step-by-step explanation:

To answer questions like these it helps to work backwards. We know that sales tax is an added percentage of the cost of a product onto total.

So we get this sort of image:

Total = Original Cost x (1 + %tax)

Now we can start putting the numbers from the question into this equation.

So we know the total:

27.50 = Original Cost x (1+%tax)

We know the original cost. It must be the total amount minus the amount of sales tax put on it. (27.50 - 1.65 = 25.85)

27.50 = 25.85 x (1+%tax)

Now we can start solving for "%tax".

(27.50/25.85) = 1 + %tax

1.0638 = 1 +%tax

1.0638 - 1 = %tax

0.0638 = %tax

6.38% = tax

The sales tax is 6.38%.

19
The diagram shows a quadrilateral JKLM.
7 cm
K
J
4.5 cm
M
15 cm
L
Work out the size of angle KLM.
Give your answer correct to 3 significant figures.

Answers

Answer:

Step-by-step explanation:

Can you please help me quickly!!

Answers

Answer:

to struggle to succeed when chances are bad

Step-by-step explanation:

She got nervous and froze when she thought she was going to lose.

What is the value of the expression when n = 3?

-2n(5+n-83n)

Answers

-2x3 (5+3-83x3) then just put that in a calculator or do it in your head

An employee receives a 2% raise once per year. If the employee's initial salary is $69,400.00, what will the employee's salary be after 17 years?
Please put in answers with no commas and round to 2 decimal places.

Answers

Step-by-step explanation:

first fine 2% of the initial salary since he is paid that every year

2/100×69400=2×694=1388

so for 17 years = 1388×17

=23596

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