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.
Find the solution set.
The solution set for 512 - 125 = 0 is
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, ?
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?
Answer:
47.36
Step-by-step explanation:
i did the work
3(4x + 10) = 12x + 20
How many solutions does this equation have ?
A zoo requires that 1 adult accompany every 7 students that visit the zoo. How many adults must accompany 28 students?
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
Which of the following uses scientific notation
incorrectly?
(View picture)
13x = 17 divided by 13
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.
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?
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.
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!
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?
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
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!
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
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.
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 ..
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)
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
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]
how do I graph -x-6?
A rectangle has a perimeter of 60 inches and a base of 11 inches. What is the height?
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).
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
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?
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
Answer:
b
Step-by-step explanation:
Find the slope of the line (-2,3) (2,-3)
i need help with this problem
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
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
Answer:
5
Step-by-step explanation:
4x-x=17-2
3x=15I:3
x=5
i think thats right