Jean works for the government and was conducting a survey to determine the income levels of a number of different neighborhoods in a metropolitan area. Based on national data, Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000. Jean selected three neighborhoods and determined the average income level. What is the probability that the average income level in the neighborhoods was less than $38,000

Answers

Answer 1

Answer:

0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000.

This means that [tex]\mu = 40000, \sigma = 2000[/tex]

Jean selected three neighborhoods and determined the average income level.

This means that [tex]n = 3, s = \frac{2000}{\sqrt{3}} = 1154.7[/tex]

What is the probability that the average income level in the neighborhoods was less than $38,000

This is the pvalue of Z when X = 38000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{38000 - 40000}{1154.7}[/tex]

[tex]Z = -1.73[/tex]

[tex]Z = -1.73[/tex] has a pvalue of 0.0418

0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.


Related Questions

Find the solution set.
The solution set for 512 - 125 = 0 is

Answers

Answer:

(-5,5)

Step-by-step explanation:

5v² - 125 = 0

5v² = 125

v² = 125 ÷ 5

v² = 25

v = √25

v = ±5

v = (-5,5)

An element with mass 510 grams decays by 26.3% per minute. How much of the element is remaining after 7 minutes, ?

Answers

Answer: The element is remaining after 7 minutes = 60.23 grams

Step-by-step explanation:

The equation for mass decay :

[tex]A=A_0(1-r)^t[/tex], where [tex]A_0[/tex] = initial mass, A = mass after t minutes.

Given: [tex]A_0=510\ grams[/tex]

r = 26.3% = 0.263

t = 7 minutes

[tex]A=510(1-0.263)^7\\\\=510(0.737)^7\\\\=510(0.118106123435)\approx60.23\ grams[/tex]

Hence, the element is remaining after 7 minutes = 60.23 grams

Answer:

Its the sames steps as the other answer but round the decimal instead of 60.23 do 60.2 because the ,23 is rounded to the nearest 10th i think thats how i got it right

Step-by-step explanation:

A grocery store sells a bag of 8 oranges for $5.92. What is the unit cost?

Answers

Answer:

47.36

Step-by-step explanation:

i did the work

3(4x + 10) = 12x + 20


How many solutions does this equation have ?​

Answers

There’s No solution

A zoo requires that 1 adult accompany every 7 students that visit the zoo. How many adults must accompany 28 students?

Answers

4 adults.

Take 28/7 and you get 4

Answer:

4 adaults

Step-by-step explanation:

There are 37 students on a bus the bus stops 5 times. 7 students get off at each stop how many students are left on the bus

Answers

2 are left.
37-7-7-7-7-7=2
or 7x5=35 so 37-35=2

Which of the following uses scientific notation
incorrectly?
(View picture)

Answers

The two that use scientific notion incorrectly are...

G: two places before the decimal when there should only be one.
H: there is no decimal.

13x = 17 divided by 13

Answers

Answer:

x=17/13

Step-by-step explanation:

pretty sure you just shift x alone by itself

Answer: [tex]17/13=1.30769231[/tex]

Step-by-step explanation:

Choose the equation for the line in slope-intercept form.

Answers

The answer is C I think
C is correct- process of elimination take points on the line and put in the formula and C is the only equation that works

The bases of a trapezoid are 8 yards and 16 feet. The height of the trapezoid is 12 feet. What is area of the trapezoid in square feet?

Answers

Answer:

240 sq ft

Step-by-step explanation:

First turn the 8 yards to feet my multiplying by 3. You get 24.

Then

Add the bases together to get 40 Divide them by the number of bases (2) to get 20

Multiply the 20 by the height, (12) to get 240

240 sq feet

Mark me as brainliest if this helps!

A box contains 4 red marbles, 9 white marbles, and 8 blue marbles. If a marble is randomly selected from the box, what is the probability that it is blue? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.

Answers

Answer:

8/21

Step-by-step explanation:

Add the number of marbles : 4+9+8= 21

Then how many are blue: 8

Answer 8/21. Can't be simplified

0.38

please help me.. i would really appreciate it, thank you!

Answers

The answer is C as I know

Mrs. Dawes has 4 bags of potting soil.
She uses 1 bag for a large plant and the remainder for small plants.
If each smaller plant uses 1/8
of a bag of soil, how many smaller plants can she pot?

Answers

it should be 24

4 bags - the one for the big plant
3 left so 8 plants take up one bag.
so then that should mean 24 plants can be potted with the 3 remaining bags

A cookie recipe that calls for 2 2/3 cups of sugar will make 32 cookies however you only have 1 2/3 cup of sugar and you have to adjust your recipe what fraction of the recipe

Answers

Explanation is in the file

tinyurl.com/wpazsebu

A Pastry chef has a container with 1/4 pounds of sprinkles . The chef needs to spread the sprinkles equally among five cakes . What fraction with the sprinkles will the chef be able to use on each cake? Thanks for answering have a nice 2021 and stay safe!​

Answers

Answer:

1/2 on each cake

Step-by-step explanation:

Answer:

1\2

Step-by-step explanation:

What is the median of this data set 2 2 5 6 6 8 9 11?

A) 6
B)5
C)7
D) 8

Answers

Answer:

6 is your answer since its in the middle.

Step-by-step explanation:

You randomly select ONE card from a 52-card deck. Find the probability of selecting a card greater than 2 and less than 7, or a diamond.

Answers

There is 13 diamonds and 4 numbers greater than 2 but less than 7. This means your probability of selecting one of these specific cards is a 17/52 chance

hihhhhi someone help please ..

Answers

Answer:

1. 2³

2.2⁵= 2×2×2×2×2= 32

2⁶= 2×2×2×2×2×2= 64

Step-by-step explanation:

hope it helps

Answer:

1. [tex]2^{3}[/tex]

2. It represents [tex]2*2*2*2*2[/tex] and [tex]2*2*2*2*2*2[/tex]

Step-by-step explanation:

1. it would have to be an exponent so 2*2*2 is 8 and 2^3 is also 8

2. it is an exponent so it would basically be multiplying the number times the number/amount of exponents so 2^5= 32 and 2^6=64

hope this helped :)  

h (5x)=2x^2 - 5


find h(5x)

Answers

Answer:

5x

=5*x

=x+x+x+x+x

=5x

Step-by-step explanation:

=5*x

=x+x+x+x+x

=5x

x² + 3x -4 = 0
Factor the quadratic equation

Answers

Answer:

(x-1)(x+4)

Step-by-step explanation:

[tex]x^2+3x-4\\x^2-x+4x-4\\x(x-1) 4(x-1)\\(x-1)(x+4)[/tex]

(x+4)(x-1)

First, find the factors of the constant (number without an x)

The factors of -4 are:
-1, 4
1, -4
2, -2

Looking at these factors find which pair of factors adds up to the middle number (3x)

4 + -1 = 3

Now you can factor this equation. Put x + 4 into one pair of parenthesis and x - 1 into another pair of parenthesis. You do this because you are separating the two factors into two expressions, that when multiplied together, will equal x^2 + 3x - 4

(x+4)(x-1) is the answer

To check this, multiply the two expressions together. You should get x^2+3x-4=0

how do I graph -x-6?

Answers

This is how you graph -x-6

A rectangle has a perimeter of 60 inches and a base of 11 inches. What is the height?

Answers

Answer:

19

Step-by-step explanation:

11 x 2 = 22

60 - 22 = 38

38/2 = 19

Stable cost reporting in a manufacturing setting is typically a sign that operations are running smoothly. The accounting department at Rockwell Collins, an avionics manufacturer, analyzes the variance of the weekly costs reported by two of its production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use α = 0.10 (to 2 decimals).

Answers

Answer:

Following are the responces to the given question:

Step-by-step explanation:

For this issue the statistical programme performance is:

Two overview hypothesis test sample variance:

[tex]\to \sigma_1^2[/tex]  =Population variance 1

[tex]\to \sigma_2^2[/tex] = Population variance 2

[tex]\to \frac{\sigma_1^2}{\sigma_2^2}=[/tex] Two variance ratios

[tex]\to H_0: \frac{\sigma_1^2}{\sigma_1^2}=1\\\\\to H_A: \frac{\sigma_1^2}{\sigma_1^2}\neq 1[/tex]

Following are the result of the Hypothesis test: [tex]Ratio \ \ \ \ \ \ \ \ \ \ Num.DF \ \ \ \ \ \ \ \ \ \ Den.DF \ \ \ \ \ \ \ \ \ Sample\ \ Ratio\ \ \ \ \ \ F-Stat \ \ \ \ \ \ \ P-value\\\\[/tex]

[tex]\frac{\sigma_1^2}{\sigma_1^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1091[/tex]

Test statistic [tex]= 2.3478 \approx 2.35[/tex]

P-value > 0.10

The null hypothesis should not be rejected.

4x + 3 − 23x

This expression has 3 terms.
true or false

Answers

Answer:

True

Terms are separated by the signs

Maitland multiplies 0.05 x 0.8 on a calculator. The calculator shows a product of 0.04. Maitland says the calculator must be broken because multiplying tenths by hundredths give a product in the thousandths.

Is the calculator broken?

Answers

Answer:

no, the calculator is not broken

Step-by-step explanation:

its not broken i got the same answer your welcome

Maria bought a bag of mixed fruit that is 40% oranges, 33% green apples, and 27% red apples, If she
randomly selects 5 pieces of fruit from the
bag, how many would you expect to be oranges?
A 1
B 2
C 3
D 4

Answers

Answer: B

Explanation

Answer:

b

Step-by-step explanation:

Find the slope of the line (-2,3) (2,-3)

Answers

(2,-3) is the answers

i need help with this problem

Answers

9514 1404 393

Answer:

  (a)  4 in²

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height of the prism.

We can find the area of the base by solving for B.

  B = V/h

  B = (12 in³)/(3 in)

  B = 4 in² . . . . . . . . . . matches the first choice

A square picture frame with each side length represented by 3x -
5 has a perimeter of 52 inches. Which equation models this situation?
A. 3x - 5 + 4 = 52
B. 3x - 5 = 52
C. 4(3x + 5) = 52
D. 4(3x - 5) = 52

Answers

Answer:

D. 4(3x-5) = 52

Step-by-step explanation:

52 is equal the sum of one side multiplied by 4

So

4(3x-5) = 52

Is the right answer

4x+2-x=17

Solve the equation for x

Explain how

Answers

3x+2=17

17-2=15

15/4 =3.75

X=3.75

Answer:

5

Step-by-step explanation:

4x-x=17-2

3x=15I:3

x=5

i think thats right

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