g The pH measurements of water specimens from various locations along a given river basin are Normally distributed, with mean 8 and standard deviation 0.3. You take water specimens from four randomly selected locations on this river basin. What is the probability that the mean pH measurement of these four specimens is greater than 8.2
Answer:
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
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.
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.
Mean 8 and standard deviation 0.3.
This means that [tex]\mu = 8, \sigma = 0.3[/tex]
Sample of 4:
This means that [tex]n = 4, s = \frac{0.3}{\sqrt{4}} = 0.15[/tex]
What is the probability that the mean pH measurement of these four specimens is greater than 8.2?
This is 1 subtracted by the pvalue of Z when X = 8.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 8}{0.15}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a pvalue of 0.9082
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
1) A basket contains six apples and five
peaches. You randomly select a piece of
fruit and then return it to the basket. Then
you randomly select another piece of fruit.
The first piece of fruit is an apple and the
second piece is a peach.
A) Dependent B) Independent
HE
FEN
Step-by-step explanation:
are you sure that math cauz that looks difficult or maybe its the fact that I'm in the 4th grade
Alvin is 7 years younger than Elgas. The sum of their ages is 63. What is Elgas age?
Answer:
Elgas is 35.
Step-by-step explanation:
Let's set up an equation.
Alvin is 7 years younger than Elgas.
A = E - 7
The sum of their ages is 63.
A + E = 63
Let's use substitution.
Plug in the first equation of A into the second equation.
A + E = 63
(E - 7) + E = 63
Combine like terms.
2E - 7 = 63
Add 7 to both sides.
2E = 70
Divide both sides by 2.
E = 35
Elgas is 35.
Hope this helps!
Bianca bought a pack of rechargeable batteries for
$9.99. If the sales tax on the batteries is 3% and Bianca
pays with $11 cash, how much change will she get back?
hi
price all taxes included is : 9.99 + 0.03*9.99 ≈ 10.29
So change is : 11 - 10.29 = 0.71
Answer:
acualy you would divide 9.99 by 3
5.
Convert each of the following fractions to a decimal using long division.
13
32
A.
B.
0
8
What is the mean absolute deviation if the mean is 15 and the majority of the data falls between 5 and 25
I need a little help. Stuck in the problem in khan academy and can’t really find and answer. 6 x 4 + 2 x 9/3
Answer:
the answer is 30
Step-by-step explanation:
1: (6*4)+(2*9/3)
2: (6*4)+(2*3)
3: 24+6
4: 30
Answer:
30
Start by multiplying then dividing
PLEASE HELPPO?!!!! Look at the attachment below
Answer:
157
Step-by-step explanation:
just trust me bro
5.6(x - 3) = -0.4x + 19.2
Answer:
Step-by-step explanation:
Answer:
this is the answer hope it helps
I NEED HELP LIKE ASAP PLS!!!!
Answer:
formula 3 only
Step-by-step explanation:
formula for the are of a circle is [tex]A=\pi r^{2}[/tex]
the other 2 formulas are the ones for circumference
HELPPPPP plssssssssss
do you even put attention in class or the teacher not showing shi but alright the answer is x=0
Find the area of the triangle. Enter your answer in the box.
9514 1404 393
Answer:
168 mm²
Step-by-step explanation:
The area of a triangle is half the product of the base and height. The height is measured perpendicular to the base.
A = 1/2bh
A = 1/2(14 mm)(12 mm)
A = 84 mm²
The area of the triangle is 84 square millimeters.
Answer:
84 whoop lololol
Step-by-step explanation:
84 mm power 2
An ice cream come has the following dimensions. What is the amount of ice cream you can fit inside the cone...
Diameter: 3 inches
Height: 6 inches
Step-by-step explanation:
Volume = 42.39
What is 5/6 of 1/2 on a number line
Answer:
5/12
Step-by-step explanation:
5/6 of 1/2 is basically 5/6 times 1/12 which is 5/12.
Find the area of the trapezoid 10ft, 7.5ft, and 13.5ft
1) 22 oz =
Ibs
oz. plz help with this one
Answer:
1.375 lbs
Step-by-step explanation:
Can you help me?! I would really appreciate it
Answer:
(3 , 8)
Step-by-step explanation:
Answer:
(3,8)
Step-by-step explanation:
the pattern of an ordered pair is (x,y). If x=3, and y=8, then you would get (3,8).
In this experiment researchers randomly assigned smokers to treatments. Of the 193 smokers taking a placebo, 29 stopped smoking by the 8th day. Of the 266 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day. Calculate the estimated standard error for the sampling distribution of differences in sample proportions.
Answer:
The estimated standard error for the sampling distribution of differences in sample proportions is 0.0382.
Step-by-step explanation:
To solve this question, we need to understand the Central Limit Theorem and subtraction of normal variables.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances:
Of the 193 smokers taking a placebo, 29 stopped smoking by the 8th day.
This means that:
[tex]p_S = \frac{29}{193} = 0.1503[/tex]
[tex]s_S = \sqrt{\frac{0.1503*0.8497}{193}} = 0.0257[/tex]
Of the 266 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
This means that:
[tex]p_A = \frac{82}{266} = 0.3083[/tex]
[tex]s_A = \sqrt{\frac{0.3083*0.6917}{266}} = 0.0283[/tex]
Calculate the estimated standard error for the sampling distribution of differences in sample proportions.
[tex]s = \sqrt{s_S^2 + s_A^2} = \sqrt{0.0257^2 + 0.0283^2} = 0.0382[/tex]
The estimated standard error for the sampling distribution of differences in sample proportions is 0.0382.
Which scenario could be represented by the algebraic expression n minus 13? Ariel wants to find the difference of a number and 13. Ariel wants to find the product of 13 and a number. Ariel wants to find the sum of a number and 13. Ariel wants to find the difference of 13 and a number. HELPPPPP
Answer is in a photo. I can only upload it to a file hosting service. link below!
bit.[tex]^{}[/tex]ly/3a8Nt8n
Answer:
a
Step-by-step explanation:
What is the diameter of the circle? Be careful here... its asking for diameter!!!
64m
8m
16m
pls help me giving brainless.
Answer:
five and three ninths
six and seven tenths
nine and one fifth
Kenny and Ben start competing businesses selling hats. Kenny buys supplies, costing $3, before he starts selling his
hats for $0.50 each.
Ben sells his hats for $0.25 each and spent only $1 on supplies. At
what point have they sold the same number of hats and made the
same profit (income minus costs)?
Write your answer as a coordinate point (hats, profit). HELP PLZ WHAT ARE THE EQUATIONS??
9514 1404 393
Answer:
(8, 1)
Step-by-step explanation:
Let x represent the number of hats sold by each seller.
__
Kenny's cost: $3
Kenny's revenue: $0.50x
Kenny's profit = revenue - cost: y = 0.50x -3
__
Ben's cost: $1
Ben's revenue: $0.25x
Ben's profit = revenue - cost: y = 0.25x -1
__
The profit and sales will be the same when the same (x, y) values satisfy both profit equations.
y = 0.50x -3
y = 0.25x -1
0.50x -3 = 0.25x -1 . . . . . substitute for y
0.25x = 2 . . . . . . . . . . . add 3-0.25x
x = 8 . . . . . . . . . . multiply by 4
y = 0.25x -1 = 2 -1 = 1 . . . using Ben's profit equation
The profit and sales will be the same for ...
(hats, profit) = (8, 1)
If 25% is 14, what is 100%?
Answer:
56
Step-by-step explanation:
25% = 14
Therefore,
25%*4 = 14*4
100% = 56
what is 10% of 100,
000
Answer:
10,000
Step-by-step explanation:
The radius of each semicircle in the composite figure is x units. The width of the rectangular part of the figure is equal to the radius.
Which expression represents the distance around the composite figure
A. 6x+2πx
B. 6x +4πx
C. 10x +2πx
D. 10x +4πx
Answer:
A) 6x + 2πx
Step-by-step explanation:
left side of figure = 4x
top and bottom flat portion of figure = 2x
2 semi-circles with radius of x is equal to 1 full circle with diameter = 2xπ
distance around = 4x + 2x + 2xπ or 6x + 2πx
Part A
Sara is making 3 batches of chocolate chip cookies and 3 batches of oatmeal cookies. Each batch of chocolate chip cookies uses 2 1/4 cups of flour. She will use 12 3/4 cups of flours of flour for all six batches.
Part B
Determine how many cups of flour are needed for each batch of oatmeal cookies.
Answer:
17 / 8 cups of flour
Please consider marking brainliest.
Write an exponential function =for a graph that passes through (2,1) and (3,10). Ill give you whatever please help
Answer:
[tex]y = \frac{1}{100} \times 10{}^{x} [/tex]
Step-by-step explanation:
Use coordinates (2,1) and 3,10
The exponential equation is
[tex]y = a \times b {}^{x} [/tex]
Plug in the x and y values.xfor both functions of coordinates.
[tex]1 = a \times b {}^{2} [/tex]
[tex]10 = a \times b {}^{3} [/tex]
Divide the equation with the larger exponet by the other equation.
[tex]10 = b[/tex]
Substitute that in for one of the equations.
[tex]10 = a \times 10 {}^{3} [/tex]
Solve for a.
[tex]10 = a \times 1000[/tex]
[tex] \frac{1}{100} = a[/tex]
So our exponetial equation is
[tex]y = \frac{1}{100} \times 10 {}^{x} [/tex]
-0.5
0
1
-2
1.5
Where is Point D on the number line?
?
Answer:
Its -1.9 for where point D is
Charlie took a test with two parts; Reading with 60 questions and Math with 40 questions. He scored 55% on the Reading part and 90% on the Math part. What is his overall percentage score, assuming each of the 100 questions has equal weight?
Answer:
10
Step-by-step explanation:
Can someone please help me find the area.
Answer:
51 ft²
Step-by-step explanation:
The figure is composed of two different triangles (triangle 1 and 2) and a rectangle
Area of the composite figure = area of triangle 1 + area of triangle 2 + area of rectangle
✔️Area of triangle 1 = ½*bh
b = 3 ft
h = 2 ft
Area of triangle 1 = ½*3*2 = 3 ft²
✔️Area of triangle 2 = ½bh
b = 3 ft
h = 3 ft
Area of triangle 2 = ½*3*3 = 4.5 ft²
✔️Area of rectangle = L*W
L = 3 + 8 = 11 ft
W = 4 ft
Area of rectangle = 11*4 = 44 ft²
✅Area of the composite figure = 3 + 4 + 44
= 51 ft²
