The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.

Answers

Answer 1

Answer:

a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) The 25th percentile of the sample mean is of $2596.

d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

If |Z|>2, the measure X is considered unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.

This means that [tex]\mu = 2630, \sigma = 500[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]

a) What is the probability that the sample mean rent is greater than $2700?

This is the 1 subtracted by the p-value of Z when X = 2700. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{2700 - 2630}{50}[/tex]

[tex]Z = 1.4[/tex]

[tex]Z = 1.4[/tex] has a p-value 0.9192

1 - 0.9192 = 0.0808

0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) What is the probability that the sample mean rent is between $2450 and $2550?

This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.

X = 2550

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

[tex]Z = \frac{2550 - 2630}{50}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a p-value 0.0548

X = 2450

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

[tex]Z = \frac{2450 - 2630}{50}[/tex]

[tex]Z = -3.6[/tex]

[tex]Z = -3.6[/tex] has a p-value 0.0002

0.0548 - 0.0002 = 0.0546.

0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) Find the 25th percentile of the sample mean.

This is X when Z has a p-value of 0.25, so X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 2630}{50}[/tex]

[tex]X - 2630 = -0.675*50[/tex]

[tex]X = 2596[/tex]

The 25th percentile of the sample mean is of $2596.

Question d and e)

We have to find the z-score when X = 2645.

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

[tex]Z = \frac{2645 - 2630}{50}[/tex]

[tex]Z = 0.3[/tex]

|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.


Related Questions

There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour).

What does the slope of the line represent?
A. the change in wind speed for every 1 kPa increase in air pressure
B. the wind speed of a hurricane with an air pressure of 1000 kPa
C. the wind speed of a hurricane with an air pressure of 0 kPa
D. the change in wind speed for every hour

Answers

Answer:

A. the change in wind speed for every 1 kPa increase in air pressure

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the slope (rate of change) of the line and b is the y intercept (value of y when x = 0)

Given the line y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots.

The slope of the line is -1.22. The slope means that there is a decrease in wind speed by 1.22 miles per hour for every increase of 1 kPa in air pressure.

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/1+x a=2

Answers

If f(x) = 7/(1 + x), then

f (2) = 7/3

f '(x) = -7/(x + 1)²   ==>   f ' (2) = -7/9

f ''(x) = 14/(x + 1)³   ==>   f '' (2) = 14/27

f '''(x) = -42/(x + 1)⁴   ==>   f ''' (2) = -14/27

Then the Taylor series of f(x) about a = 2 is

7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³

= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³

Find the area of a rectangle that measures 12ft by 3 1/3 ft

Answers

Answer:

40 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

   =12 * 3 1/3

Change to an improper fraction

   = 12 ( 3*3+1)/3

   = 12 (10/3)

     40

Answer:

[tex]40 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = l \times b \\ = 12 \times 3 \frac{1}{3} \\ = 12 \times \frac{10}{3} \\ = \frac{120}{3} \\ = 40 {ft}^{2} [/tex]

An elevator is on the twelfth floor it goes down 11 floors and than up 5 floors what floor is the elevator on now

Answers

Answer:

The sixth floor

Step-by-step explanation:

the answer is that it's on the 5th floor now

Rewrite the function f(x)=16^x in four different ways, using a different base in each case.

Answers

Answer:

X=1

f(x)=16^1

=16

X=2

f(x)=16^2

256

X=3

f(x)=16^3

=4096

X=4

f(x)=16^4

=65536

Here are four different ways to rewrite the function f(x) = 16^x, using a different base for each case:

Using base 2:

f(x) = (2^4)^x = 2^(4x)

Using base 3:

f(x) = (3^2)^x = 3^(2x)

Using base 10:

f(x) = (10^(log10(16)))^x = 10^(log10(16) * x)

Using base e (natural logarithm):

f(x) = (e^(ln(16)))^x = e^(ln(16) * x)

How to explain the function

In these rewritten forms, the exponentiation of the base is expressed as a simpler expression.

This involves the new base, which helps to illustrate the relationship between the original function and the different bases used.

Learn more about functions

https://brainly.com/question/11624077

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An item is regularly priced at$15.It is now priced at a discount of55%off the regular price

Answers

Answer:

$6.75

Step-by-step explanation:

The regular price is $15 dollars. The discount is 55% off the $15.

15 * 0.55 = 8.25

15 - 8.25 = 6.75

Hope this helps.

Answer:

discount =8.25

New price 6.75

Step-by-step explanation:

15 is the regular price

The discount is 55%

15*.55

8.25

The new price is the regular price minus the discount

15-8.25

6.75

round 3/5 to 3 decimal points

Answers

Answer:

3/5=0.600

Step-by-step explanation:

I hope this answer helps

The answer is 0.6.

Upto 3 decimal places it is 0.600.

Determine the area of the given parallelogram with length 11 and altitude five

Answers

9514 1404 393

Answer:

  55 square units

Step-by-step explanation:

The area of a parallelogram is the product of base length and height:

  A = bh

  A = (11)(5) = 55 . . . area of the given parallelogram in square units

when solving inequalities,name 2 steps that are the same as solving equations and one difference

Answers

9514 1404 393

Explanation:

same:

the addition property of equalitythe multiplication property of equality (for positive multipliers)

different:

the multiplication property of equality for negative multipliers

_____

Additional comment

Multiplication by a negative number has the effect of re-ordering numbers:

  -1 < 2 . . . 1 > -2 (both sides multiplied by -1)

Other functions can have the same effect, so care must be taken when applying functions to both sides of an inequality.

  1/2 > 1/3 . . . 2 < 3 (reciprocal function applied to both sides)

  30° < 60° . . . cos(30°) > cos(60°) (cosine function applied to both sides)

if (a + b) = 73 and a b =65 find value of a²+ b²​

Answers

Step-by-step explanation:

Here,

by formula a^2+b^2=(a+b)^2-2ab

so,

or,(a+b)^2-2ab

or,(73)^2-2×65

or,5329-126

=5203 is the answer

Which inequality is shown in the graph?
I need help plz

Answers

Answer:

I am pretty sure it is B.

Step-by-step explanation:

This is a line with a positive slope, therefore we can discard c and d.

the sign < will mean that the shaded in area will be on your right side.

A certain prescription drug diminishes in the system at a rate of 25% per hour. If a person was administered 1450mg of the drug, how much will remain in 4 hours? How many hours will it take for the amount of the drug in their system to be less than 5mg?

Answers

9514 1404 393

Answer:

459 mgabout 20 hours

Step-by-step explanation:

The decay factor is 1 -25% = 0.75 per hour, so the exponential equation can be written ...

  r(t) = 1450·0.75^t . . . . . milligrams remaining after t hours

__

a) After 4 hours, the amount remaining is ...

  r(4) = 1450·0.75^4 ≈ 458.79 . . . mg

About 459 mg will remain after 4 hours.

__

b) To find the time it takes before the amount remaining is less than 5 mg, we need to solve ...

  r(t) < 5

  1450·0.75^t < 5 . . . . use the function definition

  0.75^t < 5/1450 . . . . divide by 1450

  t·log(0.75) < log(1/290) . . . . . take logarithms (reduce fraction)

  t > log(1/290)/log(0.75) . . . . . divide by the (negative) coefficient of t

  t > 19.708

It will take about 20 hours for the amount of the drug remaining to be less than 5 mg.

The population of a strain of bacteria doubles in a culture. At noon there were 80 bacteria present and by 4:00 PM there were 20 480 bacteria. Determine algebraically the doubling period. Hint: You DO NOT need to use systematic trials.

Answers

Answer:

t = 1/2 hour

Step-by-step explanation:

20480 = 80[tex]x^{t }[/tex]

20480 = 80[tex]x^{4 }[/tex]

20480/80  =  [tex]x^{4 }[/tex]

256 =  [tex]x^{4 }[/tex]

x = 4

doubling period

2 = [tex]4^{t}[/tex]

t = 1/2 hour

Find x please explanation need it

Answers

Cos 19 = Adjacent/hypotenuse
(Cos 19)(21) = 19.9

Your calculator is showing a result of 248.592.
What is this to the nearest whole number?

Answers

the nearest whole is 200.600
200.600 should be the nearest whole

I am authoring you to offer free insurance for a year the regular price is 6.99 this will save the customer almost_ a year

Answers

6.99*12 = $83.88 savings an year

Please help due tomorrow

Answers

Answer: x= 2.5, y = 10

Step-by-step explanation:

I'm going to assume that these photocopies are proportional in relations to each other.

If they're proportional, you can set up two proportions:

[tex]1) \frac{x}{5} =\frac{3}{6} \\\\2) \frac{5}{y} =\frac{3}{6}[/tex]

And cross-multiply:

[tex]1) 6x = 5*3 \\\\2) 3y = 5*6[/tex]

Then solved for x and y:

[tex]1) 6x = 15\\x=\frac{15}{6} =\frac{5}{2} =2.5 \\\\2) 3y = 30\\y=\frac{30}{3} =10[/tex]

Hari earns Rs 4300 per month. He spends 80% from his income. How much does he save in a year? ​please give answer in step by step explaination​

Answers

Answer:

4300 x 12= 51600

20/100 x 51600

10,320 Rs  (also pay bohat kam hai :D )

Think of a two-digit number. What is the probability that it has different digits?

Answers

Answer:

9/10

Step-by-step explanation:

The first two digit number is 10 and the last is 99. That's a total of 99-10+1 numbers in all. That simplifies to 90. (Just like if we wanted to see how many numbers was 3,4,5, we would do 5-3+1=3 to get the total number.

Anyways, let's consider first how many 2 digjt numbers whose digits are equal. You have 11 22,33,44 55,66,77,88,99 which is 9 numbers total.

So the amount of 2 digits number whose digits differ is 90-9=81.

The probability that a 2 digit number have different digits is 81/90.

This can reduce. Divide top and bottom by 9 giving 9/10.

d) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal for 99% of the products to exceed 10000 hours before failure

Answers

Solution :

Let the probability laser works = p

The probability that the system works = [tex]$P(\text{all three component works}) = p^3 $[/tex]

                                                                                                                   = 0.99

Therefore, p = 0.9967

Now for the above probability critical z = -2.72

Hence, the mean life is equal to = [tex]10,000 + 2.72 \times 600[/tex]

                                                     = [tex]10,000+1632[/tex]

                                                     [tex]=11,632[/tex]

A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of a new function compare to the domain and range of the original function?

Answers

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

Which of the following scatterplots do not show a clear relationship and would not have a trend line?

Answers

Answer:

the second one

Step-by-step explanation:

it is not going in any general direction

Answer:

B

Step-by-step explanation:

What is the slope of the line that contains these points? xxx 454545 494949 535353 575757 yyy 101010 555 000 -5−5minus, 5 slope:

Answers

Answer:

-5/4

Step-by-step explanation:

Given :

x : 45, 49, 53, 57

y : 10, 5, 0, - 5

The slope of the line :

Slope = Rise / Run

y2 = - 5, y1 = 10

x2 = 57, x1 = 45

Rise = y2 - y1 = - 5 - 10 = - 15

Run = x2 - x1 = 57 - 45 = 12

The slope = Rise / Run = - 15 / 12 = - 5/4

Answer:

-1

Step-by-step explanation:

i brought the answer correct

obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the progression.​

Answers

If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which

x - 5 = r (x + 1)

==>   r = (x - 5) / (x + 1)

and

x - 2 = r (x - 5)

==>   r = (x - 2) / (x - 5)

Then

(x - 5) / (x + 1) = (x - 2) / (x - 5)

Solve for x :

(x - 5)² = (x - 2) (x + 1)

x ² - 10x + 25 = x ² - x - 2

-9x = -27

x = 3

It follows that the ratio between terms is

r = (3 - 5) / (3 + 1) = -2/4 = -1/2

Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by

a(n) = 4 (-1/2)ⁿ⁻¹

The sum of the first 12 terms - denoted here by S - is then

S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹

Solve for S :

S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]

(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]

==>   S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]

==>   3/2 S = 4 (1 - 1/4096)

==>   S = 8/3 (1 - 1/4096)

==>   S = 1365/512

Question 4 please provide explanation for question

Answers

Answer:

A

Step-by-step explanation:

We need to find a equation that is where the domain is all real numbers and the range is all real numbers greater than -3

A square root function cannot equal to all real numbers because we cant take the square root of a negative number. so B and C are already wrong.A cubic function range is all real numbers. so y can be greater than -3 but it would also include. values lesser than -3. so D is Wrong.

A is right, the domain of a absolute value function is all real numbers. The range of a absolute value is all numbers greater than or equal to zero but if we subtract 3, it changes into all real numbers greater than or equal to -3

what is x divided by one​

Answers

Answer:

[tex] x \div 1[/tex]

[tex] = x[/tex]

Answer:

[tex]x\div 1=x[/tex]

Step-by-step explanation:

When x is divided by one it is called reciprocal.

reciprocal is the inverse of a number or a value.

examples: The reciprocal of 3 is 1/3, and the reciprocal of 5 is 1/3.

OAmalOHopeO

How many of 320 million Americans would you predict wear contact lens

Answers

Answer:

I think 40 - 60 Million Americans would wear contact lenses.

if( x) means 10 what's (x) divide my 2​

Answers

Answer:

If you meant that the value of (x) is equal to 10, and you want that value divided by 2, then that would be easy!

10/2 is equal to 5.

If you meant something else, please let me know! :)

Find the length of BC
A. 6.81
B. 7.64
C. 13.37
D. 29.44

Answers

Answer:

13.37 = BC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = opp / hyp

cos 27 = BC / 15

15 cos 27 = BC

13.36509 = BC

Rounding to the nearest hundredth

13.37 = BC

Helpekksdjfkfodldkdkdodidididisj Help

Answers

Answer:

The answers to your questions are given below.

Step-by-step explanation:

1. m∠1 and m∠2 are complementary. This statement was given from the question.

2. m∠1 + m∠2 = 90°. Complementary angles add up to give 90°.

3. m∠2 = 74°. This was given in the question.

4. m∠1 + 74 = 90°. Since m∠1 and m∠2 are complementary. Their sum will add up to give 90°

5. m∠1 = 16°

We can prove m∠1 = 16° as shown below:

m∠1 + m∠2 = 90° (complementary angles)

m∠2 = 74°

m∠1 + 74 = 90°

Collect like terms

m∠1 = 90 – 74

m∠1 = 16°

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