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
Mr. Esposito is 5 foot 11 inches tall. Mrs. Humbert is 63 inches tall. Who is taller and by how much?
Answer:
Mr. Esposito is taller By 8 inches
Step-by-step explanation:
5 feet and 11 inches is equal to 71 inches. And 71 inches is greater than 63 inches. Therefore, Mr. Esposito is taller.
(71-63=8)
DON'T FORGET TO DOUBLE-CHECK!
Answer:
Mr. Esposito is taller by 8 inches
Step-by-step explanation:
Mr. Esposito
12x5 = 60 + 11 = 71
Mrs. Humbert
63 inches = 5 foot and 3 inches
71 - 63 = 8
Based on the graph, How many calories are in 1 piece of candy?
A:1/20
B:1/15
C:15
D:60
There are 3 flag stamps and 7 follower stamps in Noelle’s stamp collection. What is the ratio of flower stamps to flag stamps
Answer:
3:7 or 3/7
Step-by-step explanation:
if it helps don't forget to like and mark me
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below.
A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.
Which interval contains the median water bill?
$150–$175
$175–$200
$200–$225
$225–$250
The interval which contains the median water bill is $200 - $225
The tabulated data :
Class interval ____ Frequency ___ Cummulative frequency
100 to 125, ________ 1 ___________ 1
125 to 150, 2 ______ 2 ___________3
150 to 175, 5 _______5 ___________8
175 to 200, 10 ______10 __________18
200 to 225, 13 _____13 __________ 31
225 to 250, _______ 8 __________40
The median class = Cummulative frequency / 2
The median class = 40 / 2
The class interval which contains the 20th frequency.
This is the 200 - 225 class
The interval which contains the median water bill is $200 - $225
Learn more : https://brainly.com/question/300591
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Round it to the nearest tenth
Answer: so i got 31 but if you round it it will be 30 hope it helps
Step-by-step explanation:
Look at the two quadrilaterals shown below.
Which one of the following statements about these quadrilaterals Is FALSE?
Both quadrilaterals have four equal angles.
Both quadrilaterals have four equal sides.
Both quadrilaterals have opposite parallel sides.
Both quadrilaterals have four right angles. The two shapes are a square and a rectangle
Answer:
"Both quadrilaterals have four equal sides."
Step-by-step explanation:
This statement is only true for a square since as we all know it has four equal sides, but a rectangle has two parallel sides that are equal to each other but on the other two parallel sides, they must differ in length.
Answer:
"Both quadrilaterals have four equal sides." is the false statement
Step-by-step explanation:
helppppp it timeddddd quickkkkkkk i give brainlyist toooo
Answer:
Hello, I believe the answer would be PK since both XS and PK are the same height.
Step-by-step explanation:
I hope this helped you!
Answer:
option A
PK corresponds to XS
Find the general term of series 1/2-1+2-4+
For the given sequence the general term could be defined as n/(n + 1), where 'n' is clearly a natural number.
Zoe collects dinosaur models. she has 912 models and keeps them in different shoe boxes Zoe keeps 24 dinosaurs in each box how many boxes of dinosaurs does she have
Answer:
Zoe has 38 boxes.
Step-by-step explanation:
I found this answer by dividing 912 by 24 (912/24).
I hope this helped.
helppppppppp m eeeee plzzzzzzz
Dr. Seals borrows $15,000 to remodel her backyard. The interest rate is 3%. The interest is compounded twice a year for two years.
Answer:
what is the question?
Step-by-step explanation:
f the distance between two points is 9 and point one is located at (-2, 2), what could be the possible coordinates of point two?
(2, 9)
(7, 2)
(11, 2)
(2, 11) HELP NOW
A normal six sided die is thrown once the number of outcomes in the sample is
Answer:
1/6
Step-by-step explanation:
Since it's a six sided die there's 6 different sides the die could land on the probability of landing on certain number depends on how much you roll the die.
For example: you roll the die 10 times and you land on 3, 5 times. the probability landing on 3 was 5/10 or 50%
If you have 8 marbles in the bag (5 blue and 3 green) and you draw 2 with replacement, what is the theoretical probability that both marbles will be green?
a.
14%
c.
23%
b.
20%
d.
39%
Answer:
d.39%
Step-by-step explanation:
Loki told me
But really, 39% should be correct
the rule for converting yards to feet
Answer:
1 yard=3 feet
Step-by-step explanation:
If it needs more, then 3 feet=36in.
A student paid 256.37 in school fees how much has he paid to the nearest hundred
Answer:
300
Step-by-step explanation:
256.37 5 and 6 is high enoughh to boost that 2 up to a 3
Answer:
uhhh 256.37 is rounded to the nearest hundreth
Unless you mean hundred thwn it would be 300
6 x (36÷12)2 + 8 = =
6*(36/12)2+8
=44
Hope this helped :T
Answer: 44
Step-by-step explanation: PEMDAS tells us to solve what’s in the parentheses, exponents, then multiply, divide, add, and subtract from left to right.
If m is an integer, then 8 x 10^m is equal to 8.
Answer:
No this is not true.
Step-by-step explanation:
An integer is a whole number and not a fraction.
An integer can be 0, 1, 3, 16, 18, 100, etc.
But an integer is either 0 - infinity.
For 8 * 10^m to equal 8, it has to be a fraction.
So, m can not be a integer. This is wrong.
Hope this helps! :)
Manny buys hot dog buns for a cookout. he needs 30 buns and he buys bags of 8 buns. how many bags does manny need?
Answer:4
Step-by-step explanation:
30÷8=3.75
3.75=4
Manny need 4 bags.
What is the surface area of the figure? 408ft^2 458ft^2 545ft^2 720ft^2
9514 1404 393
Answer:
(b) 458 ft²
Step-by-step explanation:
The total area is the sum of the L-shaped front and back areas and the areas of the 6 rectangular faces.
The front L-shaped area can be considered to be a 12 ft × 12 ft square with a 5 ft × 7 ft rectangle cut from the upper left corner. Its area is then ...
(12 ft)(12 ft) -(5 ft)(7 ft) = (144 -35) ft² = 109 ft² . . . . front area
__
The sum of the areas of the rectangular faces is the product of the width of the figure (5 ft) and the perimeter of the L-shaped face. That perimeter is the sum of the edge lengths. Starting from the lower-left corner and working clockwise, we find the perimeter to be ...
7 ft + 7 ft + 5 ft + 5 ft + 12 ft + 12 ft = 48 ft
Then the sum of rectangular face areas is ...
(48 ft)(5 ft) = 240 ft² . . . . rectangular face area
The total surface area is then ...
2×front area + rectangular face area
= 2×109 ft² +240 ft² = 458 ft² . . . . total surface area
Please help me ASAP AND explain the steps plz. Zymirah earns 5% commission on all sales at a jewelry store plus $10 an hour. Yesterday she
sold $3,200 in merchandise and earned a total of $240. How many hours does she work?
a. 8 hours
b. 12 hours
C. 32 hours
d. 160 hours
Answer:
a) 8 hours
Step-by-step explanation:
h = # hours worked
240 = .05(3200) + 10h
240 = 160 + 10h
80 = 10h
8 = h
What is the value of y in the parallelogram below
A coffee shop sells their coffee beans by the pound. the table below shows the cost in dollars for a pound of two different types of beans. How much more is the cost for 1 1/3 pounds of jimmy jitters beans then the calls for 1 1/3 pounds of Harry's himalayan beans
Answer: 23.6
Step-by-step explanation:
9.25+8.42 = 17.7
1 1/3 x 17.7 = 23.6
Five times a number is the same as 30 more than 8 times the number. Find the number. If n is "the number," which equation could be used to solve for the number? 3n = 30 5n + 8n = 30 5n = 8n + 30
Answer:
C. 5n = 8n + 30
Step-by-step explanation:
5 times a number = 5n
30 more than 8 times a number = 30 + 8n
If those expressions are equal, then:
5n = 8n + 30
Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. 2 identical solid right pyramids with square bases are connected at the square base. Another 2 are connected in the same way and are stacked on top of the other 2 pyramids. The length of the base edge is 2 feet and the height of the whole structure is 6 feet. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet. What is the volume of material he must purchase? 2 ft3 4 ft3 6 ft3 8 ft3
Im Very sorry for the bots (I hate when they do this) BUT the answer is 8ft 3 Hope it helps!!
To create an exact copy of the sculpture, the volume of material they must purchase is [tex]8\,\text{f}{{\text{t}}^{3}}[/tex].
What is the volume of a cuboid?The volume of a cuboid is calculated by multiplying its length, width, and height.
The length and width of the triangle are identical since the base is a square.
[tex]L = W = 2\,{\text{ft, and }}H = 6\,{\text{ft}}[/tex]
Knows the volume of material he must purchase,
[tex]\text{Volume}=\frac{\text{Height}\times \text{length}\times \text{width}}{3}[/tex]
So,
[tex]\Rightarrow \text{Volume}&=\frac{2\times 2\times 6}{3} \\\Rightarrow \text{Volume}&=2\times 2\times 2\,\text{f}{{\text{t}}^{3}} \\ \Rightarrow \text{Volume}&=8\,\text{f}{{\text{t}}^{3}} \\[/tex]
Therefore, the volume of material they must purchase is [tex]8\,\text{f}{{\text{t}}^{3}}[/tex].
Learn more about the volume of cuboids, here:
https://brainly.com/question/46030
The function f(x) = 600(0.981)x, where x is the time in years, models a declining lemming population How many
lemmings will there be in 3 years?
A.about 566
B.about 1,803
C.about 1,766
D.about 601
Answer:
The answer for this question is:
About 566 lemings
Step-by-step explanation:
Answer:
A.about 566
Step-by-step explanation:
Round 6,584,003 to the nearest 10,000
The answer is 6,580,000.
I hope this helped! :)
HELP PLEASEEEEEEEEEE
Answer:
[tex]\frac{4}{9}[/tex] or 0.444.... repeating
Step-by-step explanation:
[tex]\frac{1}{3}[/tex]÷[tex]\frac{3}{4\\}[/tex] = [tex]\frac{1}{3}[/tex]×[tex]\frac{4}{3}[/tex] = [tex]\frac{4}{9\\}[/tex]
PLEASE HELP I ONLY HAVE AN HOUR !!!!
Answer:
2
Step-by-step explanation:
A=[tex]\pi[/tex]r²
(19/6)[tex]\pi[/tex]=(285/360)[tex]\pi[/tex]r²
Divide both sides by pi, and they cancel out.
x is the radius, so replace r with x.
19/6=285/360x²
19/6÷285/360=x²
(19/6)·(360/285)=x²
4=x²
√4=x
2=x
Driving instructors Mr. Adams and Mr. Bateman teach class independently of each other. Among Mr. Adams’s students, 68% pass the driving test on the first try, while 74% of Mr. Bateman’s students pass the driving test on the first try. Suppose there are 40 students in Mr. Adams’s class and 50 students in Mr. Bateman’s class. Let A = the proportion of students who pass the driving test on the first try from Mr. Adams’s class and B = the proportion of students who pass the driving test on the first try from Mr. Bateman’s class. What is the probability that Mr. Bateman’s class has more students who pass on the first try?
Find the z-table here.
0.266
0.547
0.734
0.765
Answer:
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the binomial approximation to the normal and subtraction of normal distributions.
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.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Subtraction of normal distributions:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
Among Mr. Adams’s students, 68% pass the driving test on the first try. Sample of 40.
This means that [tex]p = 0.68, n = 40[/tex].
[tex]\mu_A = np = 40*0.64 = 27.2[/tex]
[tex]s_A = \sqrt{40*0.68*0.32} = 2.95[/tex]
74% of Mr. Bateman’s students pass the driving test on the first try. Sample of 50:
[tex]p = 0.74, n = 50[/tex]
[tex]\mu_B = np = 50*0.74 = 37[/tex]
[tex]s_B = \sqrt{50*0.74*0.26} = 3.1016[/tex]
What is the probability that Mr. Bateman’s class has more students who pass on the first try?
This is the probability that B - A is greater than 0.
Distribution B - A:
Mean:
[tex]\mu = \mu_B - \mu_A = 37 - 27.2 = 9.8[/tex]
Standard deviation:
[tex]\sigma = \sqrt{s_A^2 + s_B^2} = \sqrt{2.95^2 + 3.1016^2} = 4.28[/tex]
Probability of being larger than 0:
1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 9.8}{4.28}[/tex]
[tex]Z = -2.29[/tex]
[tex]Z = -2.29[/tex] has a pvalue of 0.011
1 - 0.011 = 0.989
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Answer:
0.734, c
Step-by-step explanation:
