Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1,000 observations in the data set.
a. Approximately what percentage of the observations are less than 33?
b. Approximately how many observations are less than 33?

Answers

Answer 1

Answer:

a. 97.72% of the observations are less than 33

b. Approximately 977 observations are less than 33.

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.

Mean of 25 and a standard deviation of 4.

This means that [tex]\mu = 25, \sigma = 4[/tex]

a. Approximately what percentage of the observations are less than 33?

The proportion is the p-value of Z when X = 33. So

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

[tex]Z = \frac{33 - 25}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

0.9772*100% = 97.72%

97.72% of the observations are less than 33.

b. Approximately how many observations are less than 33?

Out of 1000:

0.9772*1000 = 977.2

Approximately 977 observations are less than 33.


Related Questions

the high temperature is forecast to be 5.4 F . What is this temperature in degrees Celsius ()?

Answers

Answer:

-14c

Step-by-step explanation:

I’m using the actual values 1F = -17C so just times that by 5.4

Why is android sound louder then iPhone???
Answer ASAP

Answers

My Answer

iPhones generally have better sound and more volume than Android.

Which system of linear inequalities is represented by
the graph?
+
oyz_x+3 and 3x – y> 2
o ye}x+3 and 3x –y> 2
o y }x+3 and 3x + y> 2
O ya 4x+3 and 2x-y> 2

Answers

Answer:

o ye}x+3 and 3x –y> 2 system of linear inequalities is represented by the graph.

PLEASE LET ME KNOW IF ¡ AM WRONG!

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Option A is the correct answer.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =≤

Greater than and equal = ≥

We have,

We see that,

When we graph,

y ≥ (1/3)x + 3 and 3x - y  > 2 we get the graph shown.

y ≥ (1/3)x + 3

This inequality is positive on the y-axis.

3x - y  > 2

3x > 2 + y

This inequality is positive on the x-axis.

Thus,

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ7

a) Write 5^17 x 5^2 as single power of 5​

Answers

Answer:

When we multiply two number with the same base but different power, the power gets added.

So, the answer is:

5^17*5^2

=5^(17+2)

=5^19

Your friend was supposed to repay a loan with a loan payment of $1,000 due in 6 months and another loan payment of $1,500 due in 4 years. However, your friend agrees to make two payments that replace the originally scheduled payments. The first replacement payment of $1,250 is due in 2 years and the second replacement payment of $X is due in 3 years. Suppose the interest is 7% p.a. compounded quarterly and the focal date is 3 years from now (Year 3), your friend asks for your help to determine the size of the second replacement payment, $X. Answer the following question:

Your answer for $X at the focal date is ($BLANK)
. (Express in 2 decimals) Hint: Based on your answer in Q3 and the replacement payment in Q5, you will need to determine $X.

Note: to receive the full mark, you will use all the decimal places when performing calculations, round to 2 decimal places in your final answer, and there is no need to include other symbols such as $ and comma in your final answer.

Answers

okay okay thank you thank youuu thank you thank youu thank you thank youuu thank you thank youu thank you thank youuu thank


I WILL MARK BRAINLIEST!!!!

Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is 35 degrees. And the depth of the ocean, at that point is 250 feet. How far away is she from the reef?

Answers

Answer:

435.8 feet

Step-by-step explanation:

law of sines:

*sin 90°/1 = sin 35°/250

cross-multiply to get:

x·sin35° = 250

x = 250/sin35°

x = 435.8

*we can assume the ocean surface and the reef 250 feet below forms a 90° angle

help!

Is there alternative way in solving a arithmetic sequence?​

Answers

Answer:

[tex] { \boxed{ \blue{ \tt{last \: term : l = a + (n - 1)d}}}} \\ \\ { \boxed{ \green{ \tt{sum : s = \frac{n}{2} (2a + (n - 1)d}}}} \\ or\\ { \boxed{ \tt{ \red{sum : s = \frac{n}{2} (a + l)}}}} \\ { \bf{s \: is \: sum }} \\ { \bf{ l \: is \: last \: term}} \\{ \bf{ n \: is \: number \: of \: terms}} \\{ \bf{ d \: is \: common \: difference}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Debra bought 16 pounds of sugar for $7.
How many dollars did she pay per pound of sugar

Answers

She paid .43¢ or .44¢for each pound

When the consumer's income increases by 50% assuming other conditions are constant, the demand for good Y increases by 25%. What kind of commodity is Y?

Answers

Answer:

Normal good

Step-by-step explanation:

There are 3 basic types of commodities or goods;

i. The normal good

ii. The luxury good

iii. The inferior good

Relative to income and demand, when an increase in income causes an increase in the demand for a good, then the good is a normal good. For a normal good, the measure of the responsiveness of demand to a change in income (known as income elasticity of demand) is always greater than 0. In other words, it is positive.

If instead, an increase in income causes a decrease in the demand for a good, then the good is an inferior good. The income elasticity of demand for an inferior good is less than 0. In other words, it is negative.

When the increase in income causes a larger percentage in the demand for a good, then the good is a luxury good. Luxury goods are a special type of normal goods. The income elasticity of demand for a luxury good is greater than 1 since their is a larger percentage increase in the demand.

Income elasticity of demand is calculated by finding the ratio of the percentage increase in the demand to the percentage increase in income.

In the illustration given, the consumer's income increases by 50% causing the demand for good Y to increase by 25%. This is an example of a normal group. i.e increase in income causes an increase in the demand for good Y.

The income elasticity of demand for good Y is given as the ratio of the percentage increase in demand (25%) to the percentage increase in income (50%). Therefore, the income elasticity of demand for good Y is;

25% / 50% = 0.5

Since the income of elasticity of demand for good Y is 0.5 which is greater than 0, good Y is a normal good.

D(x, y) = (3x, 3y)
Preimage:P(1, -1), Q(2, 1), R(-2, 1)
Image: P'(,), Q'(,), R'(,)
Scale factor:

Answers

Step-by-step explanation:

I have no idea but here's thiss

There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 3/8.
There are 72 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

Answers

Answer:

27

Step-by-step explanation:

specific probability = number of specific possibilities divided by number of total possibilities.

the number of total possibilities is 72 (we can pull one out of 72).

the probability of pulling a red back is 3/8.

so, to find the actual number of specific possibilities (actual number of red balls in the overall sample size of 72) we need to bring this ratio of 3/8 to an expression of x/72.

what is the factor to turn 8 into 72 ? 9.

8×f = 72

f = 72/8 = 9

to keep the ratio unchanged in its dimension, we need to apply the same factor to 3 to get x.

3/8 × f/f = x/72

3/8 × 9/9 = x/72

3×9 / 72 = x/72

3×9 = x = 27

so, the probability ratio based on actual possibilities (number of balls available) is 27/72

=>

there are 27 red balls in the bag of total 72 balls.

1. If f(x)=4*, then which of the following is the value of f(-2)?

Answers

Answer:

what is the following

Step-by-step explanation:

which of the following are not rational numbers ? (Choose all that apply.)

A. /5
B. 0.666
C. 16/9
D. -30

Answers

9514 1404 393

Answer:

  A

Step-by-step explanation:

The square root of any integer that is not a perfect square will be irrational.

  √5 is irrational

__

Any decimal number that terminates or repeats is a rational number, regardless of sign. All of the decimal numbers shown are rational. (All terminate after a finite number of digits.)

Of course, any ratio of integers is a rational number. That's what the word "rational" means.

Find the P-value for the hypothesis test with a standardized test statistic z. Decide whether toreject the null hypothesis for the level of significance α.a. Left-tailed test, z = -1.32, α = 0.10b. Right-tailed test, z = 2.46, α = 0.01c. Two-tailed test, z = -1.68, α = 0.05

Answers

Answer:

1.) We don't reject the null

2.) We reject the Null

3.) We do not reject the null

Step-by-step explanation:

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0

A.)

Left tail , Z = - 1.32 ; α = 0.10

We can use the Pvalue calculator from Z score :

Pvalue = 0.934

Pvalue > α ; Hence, we fail to reject the null, H0

B.)

Right-tailed test, z = 2.46, α = 0.01

Pvalue from Zscore calculator ;

Pvalue = 0.0069

Pvalue < α ; Hence, we reject the null, H0

C.)

Two-tailed test, z = -1.68, α = 0.05

Pvalue from Zscore calculator ;

Pvalue = 0.093

Pvalue > α ; Hence, we fail to reject the null, H0

Ana vende productos de limpieza .Por cada $100 que venda le dan de comisión $30 .¿Cuánto ganará si vende $600?

Answers

Answer:

$180

Step-by-step explanation:

$600/$100 = 6

$600 es 6 veces $100.

Por vender $600 gana 6 veces mas que por vender $100.

6 * $30 = $180

Respuesta: $180

9. Find the length of X (in the picture) plssss I need help. (GIVING POINT'S AND BRAINLY)​

Answers

Answer:

[tex] \frac{7.5}{x } = \frac{6}{4} \\ 6x = 30 \\ x = 5 [/tex]

Alexis pls answer this question you are sooooooooooooo good at math. (Nobody else answer this, only Alexis)

Answers

Answer:

5/8

Step-by-step explanation: Keep, Change and Flip so you do 1/2 times 5/4

Answer:

5/8

Step-by-step explanation:

To divide by a fraction. multiply by the reciprocal of that fraction.

1/2 * 5/4

Multiply the fractions across.

so 1*5=5, then do 2*4= 8

5/8

Express the terms of the following sequence by giving an explicit formula. 5 , 2 , -1 , -4, -7 , .

Answers

Answer:

Step-by-step explanation:

a1=5

d=2-5=-3

[tex]a_{n}=5+(n-1)(3)\\a_{n}=5+3n-3\\a_{n}=3n+2[/tex]

A=12 because I did the test and got it right and ask me for help if needed

Given that x = 4, b=6 and c = 3. Then 3a + bc = 16. 



true or false?​

Answers

Answer:

False

Step-by-step explanation:

3a + bc = 16.

Let a=4 b=6 c=3

3(4) + 6*3 = 16

Multiply

12+18 =16

30 = 16

False

Answer:

False!

Step-by-step explanation:

There is no a variable that is given, though I'm going to assume you mean that x=4 is supposed to be a=4. If I'm mistaken, there isn't much to say about whether the statement is true or false, because there's no false statement as it'd give you a=? and you can't prove or disprove this information without more information.

If my assumption is correct, we'll first start solving this problem by substituting in the variables, which would give us: 3(4)+(6)(3)=16

Then, we'll evaluate 3(4) first, because of order of operations, which gives us 12. To reiterate the problem, we now have: 12+(6)(3)=16 From here, we can already tell this is going to be a false statement, as there is no way 6 times anything but zero will give a sum less than 6, but if you didn't catch that, we can continue with our next step.

Evaluate (6)(3) in order to get 18, in order to get: 12+18=16

And finally, we'll add. 12+18 is 30, which as we know, is not equal to 16, so that makes this statement false. 30≠16

How do I do this and what’s the answers?

Answers

Answer:

a.5years=300 rabbits

b. 50 years(multiply 50 by 300)

Step-by-step explanation:

hope this is helpful

To paint interior​ walls, a person charges 50¢ per square foot plus the cost of the paint. For a recent​ job, the paint cost ​$100 and the total bill was ​$475.
The person must have painted ____ ft^2.

Answers

Answer:

750 ft²

Step-by-step explanation:

.Given :

Charge per ft² = 50¢ = $0.5

Total cost = ((charge per ft² * number of ft²) + cost of paint)

Given that :

Paint cost = $100

Total cost = $475

Number of ft² = x

Plugging values into the equation :

475 = (( 0.5 * x) + 100)

475 = 0.5x + 100

475 - 100 = 0.5x

375 = 0.5x

x = 375 / 0.5

x = 750 ft²

Find y.
Round to the nearest tenth:
28°
х
350 ft
y
y = [? ]ft

Answers

Answer:

y = 658.3 ft

Step-by-step explanation:

Alternate angles are equal. Therefore,

Reference angle (θ) = 28°

Length of side Opposite to reference angle = 350 ft

Adjacent side = y

Apply TOA, which is:

Tan θ = Opp,/Adj

Substitute

Tan 28 = 350/y

y*tan 28 = 350

y = 350/tan 28

y = 658.3 ft (nearest tenth)

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months (INC. Magazine, February 2012). A categorical response variable showed three options: The company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.
a. Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company. At a .05 level of significance, what is your conclusion?
b. Discuss any differences in the employment plans for private and public companies over the next 12 months.

Answers

Answer:

employment plan for the next 12 months is not independent of the type of company

Step-by-step explanation:

H0 : employment plan for the next 12 months is independent of the type of company

H1 : employment plan for the next 12 months is not independent of the type of company

The Chisquare statistic, χ² :

χ² = (observed - Expected)²/ Expected

Given the data:

Observed values :

_________________ Company

Emp plan ________ private _____ public _total

Add employees _____ 37 ________ 32 __ 69

No change__________19 ________ 34 __53

Layoff employees ____ 16 ________ 42__58

Total ______________72 ________108 _ 180

The expected value counts :

(Row total * column total) / grand total

Expected Values:

27.6 ___41.4

21.2 ___ 31.8

23.2 ___34.8

Chi-Squared Values:

3.20145 ___2.1343

0.228302__ 0.152201

2.23448 ____1.48965

χ² = (3.20145 + 2.1343 + 0.228302 + 0.152201 + 2.23448 + 1.48965)

χ² = 9.440383

Degree of freedom, df (row - 1) * (column - 1) = (3-1) * (2 - 1) = 2 * 1 = 2

Pvalue from Chisquare statistic, df = 2

Pvalue = 0.008913

Since ;

Pvalue < α ; We reject the null and conclude that employment plan for the next 12 months is not independent of the type of company.

A. 3.9

B. 1.0

C. 1.7

D 3.3

Answers

Answer:

its for sure C

Step-by-step explanation:

2x-5y=22n y=3x-7 Use substitution to solve the system.

Answers

Answer:

x = 1 , y = -4

Step-by-step explanation:

2x - 5y = 22 ------- ( 1 )

y = 3x - 7      ------- ( 2 )

Substitute ( 2 ) in ( 1 ) :

2x - 5 (3x - 7) = 22

2x - 15x + 35 = 22

- 13x = 22 - 35

- 13x =  - 13

 x = 1

Substitute x in ( 1 ) :

2x - 5y = 22

2 ( 1 ) - 5y = 22

- 5y = 22 - 2

-5y = 20

y = - 4

in circle T with m angle STU=50 and ST=3 units, find the length of arc SU. Round to the nearest hundredth.

Answers

9514 1404 393

Answer:

  arc SU ≈ 2.62 . . . units

Step-by-step explanation:

The arc length is given by ...

  s = rθ

where r is the radius, and θ is the central angle in radians.

  arc SU = ST·STU = 3·(50°·π/180°) = 5π/6

  arc SU ≈ 2.62 . . . units

What is the slope of the line that passes through the points (-6, -2) and (2, -2)?

Answers

Answer:

0

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -2 - -2)/(2 - -6)

   = (-2+2)/(2 +6)

    = 0/8

   = 0

Answer:

Slope is 0

Step-by-step explanation:

Slope formula is (y2-y1)/(x2-x1)

-2 - (-2)/2 - (-6)

0/8

0

solve: In(x-2)-In(x+2)=4: explain how you got to your answer.

Answers

Answer:

No real solutions.

Step-by-step explanation:

We want to solve the equation:

[tex]\ln(x-2)+\ln (x+2)=4[/tex]

Recall that:

[tex]\displaystyle \ln a-\ln b=\ln\left(\frac{a}{b}\right)[/tex]

Therefore:

[tex]\displaystyle \ln\left(\frac{x-2}{x+2}\right)=4[/tex]

By Definition:

[tex]\displaystyle e^4=\frac{x-2}{x+2}[/tex]

Cross-multiply:

[tex]e^4(x+2)=x-2[/tex]

Distribute:

[tex]xe^4+2e^4=x-2[/tex]

Isolate the x:

[tex]xe^4-x=-2-2e^4[/tex]

Factor:

[tex]\displaystyle x(e^4-1)=-2-2e^4[/tex]

Divide. Therefore:

[tex]\displaystyle x=\frac{-2-2e^4}{e^4-1}=\frac{2+2e^4}{1-e^4}\approx-2.07[/tex]

However, note that logs cannot be negative and must be nonzero. According to the first logarithm, x > 2 and according to the second, x > -2. Since the answer is not greater than two, there are no real solutions.

Each month your cell phone company charges you $ 50 for your plan plus 3 cents for each text you send. You have $ 140 budgeted for cell phone expenses for the month. Construct an inequality to make a determination about the number of texts you can send each month. Note that you cannot send a fraction of a text. You must send _____________ _____________ texts this month in order to stay within

Answers

Answer:

3000 text messages can be sent without breaking the budget.

Step-by-step explanation:

Since each month your cell phone company charges $ 50 for your plan plus 3 cents for each text you send, and you have $ 140 budgeted for cell phone expenses for the month, to make a determination about the number of texts you can send each month the following calculation must be performed:

(140 - 50) / 0.03 = X

90 / 0.03 = X

3000 = X

Therefore, 3000 text messages can be sent without breaking the budget.

Select the correct answer.

The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis. Which equation could represent function g

the result of this transformation?

Answers

Answer:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

Step-by-step explanation:

Tangent function:

The tangent function is:

[tex]f(x) = \tan{x}[/tex]

Horizontally compressed by a factor of 1/2

Horizontally compressing by a factor of 1/2 is multiplying by 1/2. So

[tex]g(x) = \frac{1}{2}\tan{x}[/tex]

Reflected over the x-axis.

Reflecting a function over the x-axis is the same as multiplying it by -1. Then g is given by:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

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(10 x 10^-3) - (2 x 10^-6)Simplify the problem and express the answer in scientific notation. Show your work. Please help!!! Which BEST describes how a pharmacy technician labels medications?a. by adding dosage information and directions for use onto the prescription bottleb. by counting the correct number of pills and adding them to the prescription bottlec. by collecting insurance information from the customer for proper billingd. by taking a message for a pharmacist who is helping another customer find the perimeter, halla el perimetro Select the correct answer. Which characteristic is not a characteristic of plastic? OA easy to mold O'B. good conductor of heat OC. lightweight and durable OD. repels water Helllllp 30 ponitts , pls finish allll solve consult limit n(e^-n) a statement that contains an error in logic is Write the opposite of each sentence There may be a great deal of opposition to a later start time How much more would 72,300 be from 63,100? A tertiary consumer is an animal that obtains its nutrition by eating primary consumers and secondary consumers. Usually tertiary consumers are carnivorous predators, although they may also be omnivores, which are animals that feed on both meat and plant material. Function of Tertiary Consumers An adjective modifies an adverb.TrueFalse Ricardo recently experienced some difficulties with a project he was managing and the client askedfor another project manager to take over. When Ricardo's boss spoke with him to point out themistakes he had made, Ricardo was careful to not lose his temper and to listen carefully. Ricardoshowed his resilience by:A) messing up on the project.B) not caring about the project.C) keeping an open mind.D) finding mistakes in the next project manager's work. If you move a plant further and further away from a light source the level of O2 production would _______________ because the process of _____________________ slows and the process of _____________________ speeds up. Kim has left her book in the class identify the tense of the given sentence A certain first-order reaction is 27.5 percent complete in 8.90 min at 25C. What is its rate constant? please i need help What was the purpose of setting up the Public Works Administration and the Works Progress Administration? On October 1, Ebony Ernst organized Ernst Consulting; on October 3, the owner contributed $83,540 in assets in exchange for its common stock to launch the business. On October 31, the companys records show the following items and amounts. Retained earnings, October 1 as $0. Cash $12,650 Cash dividends $1,570 Accounts receivable 13,520 Consulting revenue 13,520 Office supplies 2,850 Rent expense 3,110 Land 45,940 Salaries expense 6,490 Office equipment 17,530 Telephone expense 850 Accounts payable 8,110 Miscellaneous expenses 660 Common stock 83,540Required:Using the above information prepare an October 31 balance sheet for Emst Consulting ERNST. If a sample is said to contain a 98.0% enantiomeric excess of the compound (+)-camphor, what would be the observed specific rotation if the pure (+)-camphor was found to have a rotation of 44.1?