Answer:
a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.
b) By the Central Limit Theorem, approximately normal.
c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
The mean monthly fee is $142 and the standard deviation is $29.
This means that [tex]\mu = 142, \sigma = 29[/tex]
Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.
Sample of 1500(larger than 30).
By the Central Limit Theorem
The mean is $142
The standard deviation is [tex]s = \frac{29}{\sqrt{1500}} = 0.7488[/tex]
Part b: what is the shape of the sampling distribution of x hat justify your answer.
By the Central Limit Theorem, approximately normal.
Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?
This is 1 subtracted by the pvalue of Z when X = 143. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{143 - 142}{0.7488}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a pvalue of 0.9099
1 - 0.9099 = 0.0901
0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143
Which type of climate change is most likely to lead to mass extinction in which vast numbers of species of all kinds die off? A.) A gradual change in precipitation
B.) A gradual warming
C.) A gradual cooling
D.) A very rapid change
A very rapid climate change is most likely to lead to mass extinction in which vast numbers of species of all kinds die off.
What is ECOLOGICAL SUCCESSION?An ecosystem can change its structure and composition over a particular period. This term is called ECOLOGICAL SUCCESSION.
Succession refers to the gradual change that occurs in a community over time. Succession is of two types; primary and secondary succession.
Climate change and succession are causes of change in the ocean ecosystem. Hence, the succession represents the gradual change that occurs in the structural composition of the ocean ecosystem over time.
The risk of future extinction through rapid global warming is primarily expected to occur by the interaction between the climates to which organisms are adapted in their current range and the future distribution of those climates.
Thus the correct option is D.
A very rapid climate change is most likely to lead to mass extinction in which vast numbers of species of all kinds die off.
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One number is seven more than six times another number. If the sum of the numbers is 21, find the numbers
Answer:the two numbers are 2 and 19
Step-by-step explanation:
Let one of the numbers be x
and the second be 7+ 6x
so that the sum of the two numbers which totals 21 be expressed as
x + (7+ 6x) = 21
x+ 7+6x= 21
7 + 7x = 21
7x= 14
x= 14/7 = 2
one of the numbers = 2
the other number given as
7+ 6x = 7+ 6 x 2= 7+12= 19
The numbers are 2 and 19 .
The numbers as described in the question are; 2 and 19
Solving word problemsFrom the given problem statements;
The first number = y
The second number = x
Hence, y = (7 + 6x)
Their sum is therefore;
x + 7 = 6x = 217x = 14x = 2Hence, the second number is; 7 + 6x = 7 + 6(2);
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The height of a football after it has been kicked from the top of a hill can be modeled by the equation
h = 2 (-2 -4t)(2t - 8) , where h is the height of the football in feet and t is the time in seconds. How long is the football in the air?
Answer: 5 seconds
Step-by-step explanation I tried pls don’t hate meh
Answer:
si senor I sell orange?
Step-by-step explanation:
or I wash windows?
a local pet care center pays you $8 per hour to walk dogs. last summer you worked 36.75 hours a week. what was your total weekly straight time pay for one week?
Answer:
$294
Step-by-step explanation:
8(36.75) = $294
Answer:
294
Step-by-step explanation:
8(36.75)
= $294
Brandon bought Snacks for his teams practice he bought a bag popcorn for 211 and a six pack of juice bottles of total cost before tax was 1141 right and solve an equation which can be used to determine X how much
Answer: 2.11X=11.41
X=9.3
or
211x=1141
930
Step-by-step explanation:
Answer:
Equation: 6x+2.11=11.41
Answer: x = 1.55
Step-by-step explanation:
how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound
Answer:
4
Step-by-step explanation:
1. if the mass of coffee worth $10 is 'x', then its worth is 10x, and the worth of the mixture is 5(x+20);
2. using the previous item it is possible to write the next equation:
5(x+20)=4*20+10*x; ⇒ x=4.
3. the required mass is 4 pounds.
pleaseeee help meee i dont understand
Sixteen times a number j is no less than -2
1. If a height of each of the bars in a bar graph get taller as you go from the far left to the far right, the data are:
A. skewed left
B .symmetrical
c skewed right
D. No answer text provided.
2. If the height of each of the bars in a bar graph get shorter as you go from the far left to the far right, the data are:
A. skewed left
B. symmetrical
C. skewed right
D. No answer text provide
3. If the height of the each of the bars in a bar graph as you go from the far left to the right gets taller until you reach the middle and then gets shorter as you continue to the far right, the data are:
Group of answer choices
A.skewed left
B. symmetrical
C. skewed right
D. No answer text provided.
Answer:
1. Skewed to left (negative)
2. Right skewed (positive)
3. Symmetric
Step-by-step explanation:
A number x increased by 6, and then sum is doubled
*Hana purchased 2 pairs of pants for $26.59 each and a coat for $49. She used a coupon that saved her $10. The sales tax for the purchase was $7.84. How much was the total purchase?
Answer:
$100.02
Step-by-step explanation:
*Sales tax is always applied after the discount/coupon
1. Find how much Hana had spent on pants. Since she had bought 2 pairs of pants, and they are $26.59 each, we would have to multiply 26.59 by 2. So,
26.59 times 2 is 53.18.
Hana spent $53.18 on pants
2. Find how much Hana had spent on a coat. Since she had bought 1 coat, and they are $49.00 each, we would have to multiply 49.00 by 1. So,
49.00 times 1 is 49.
Hanna spent $49 on coats
3. Find how much Hana spent on clothes. Since she spent $53.18 on pants and $49 on coats, we would have to add 53.18 and 49. So,
53.18+49=102.18
Hanna spent $102.18 on clothes
4. Find how much Hana "spent" after using the coupon. Since the problem says the coupon helps Hana save $10, we need to subtract 10 from 102.18(the total amount of money Hana spent on clothes before using the coupon). So,
102.18-10=92.18
Hanna "spent" $92.18 on clothes after using the coupon
5. Find how much was the total purchase. Sales Tax is the amount of money that needs to be added to the price. Since the price is $92.18 and the sales tax is $7.84, we need to add 7.84 to 92.18. So,
7.84+92.18=100.02
The total purchase is $100.02
choose two expression equivalent to 5 (3a+4b)
A. 15a + 4b
B 15a + 20b
C. 5a + 3a + 4b
D. 4a + 10a + b + 3b
E. 10a + 5a +b + 5b
The expression equivalent to 5(3a+4b) is option (B) 15a+20b
What is Distributive property?In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality is always true in elementary algebra.
Given,
5(3a+4b)
Apply distributive property
5(3a+4b) = 15a + 20b
Hence, the expression equivalent to 5(3a+4b) is option (B) 15a+20b
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How many solutions does
Y = 2x + 10
3y - 6x = 30
Show all work
A no solution
B one solution
C infinity solutions
Answer:
A no solution
Step-by-step explanation:
y = 2x + 10
3y - 6x = 30
3(2x+10) -6x =30
6x +30 -6x =30
6x -6x = 30-30
0=0
What is the answer to this question?
Answer:
48x - 40y +24
Step-by-step explanation:
Answer:
D (48x - 40y +24)
Step-by-step explanation:
First, you need to distribute the 8 throughout the whole equation, so 8×6x=48x, 8×-5y=-40y, and 8×3=24. Right away, you can see that the answer is D.
A line of best fit predicts that when x equals 29, y will equal 32.75, but y actually equals 32. What is the residual in this case
Answer:
The residual is 0.75
Step-by-step explanation:
Recall that the residual is the VERTICAL distance between the y-value of the data point and the y-value of the predicted line. This distance can be calculated using the absolute value of the difference between these y-values.
Therefore, in our case the residual is: |32 - 32.75| = |-0.75| = 0.75
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How can you tell if a relationship is nonproportional? Select all that apply.
is the same for all ordered pairs.
is NOT the same for all ordered pairs
The graph does NOT go through the point (0,0
The graph goes through the point (0,0).
Answer:
is NOT the same for all ordered pairs
The graph does NOT go through the point (0,0
Step-by-step explanation:
TRUST me
tom wants to but a stereo that cost $540.00. he has saved 1/3 of the cost. how much gas tom saved?
What does b stand for 11.3 > b/4.3
Answer:
b = 45.69
Step-by-step explanation:
5 x 5 = 25
25 x 2 & and a half = 45.69
In the inequality expression "11.3 > b/4.3," the variable "b" represents an unknown numerical value.
In the inequality 11.3 > b/4.3, b is the variable.
The inequality is stating that 11.3 is greater than the result of dividing "b" by 4.3.
The purpose of the inequality is to compare the value of 11.3 with the value of "b/4.3" and determine if 11.3 is greater or not.
The variable "b" can take any value that satisfies the inequality.
Hence, in the inequality b stands for unknown value or variable.
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I need help dudessss
Answer:
3.618
Step-by-step explanation:
10^4=$10,000
36180/10000= 3.618
HELP PLS ASAP 50 POINTS HELP ILL MARK BRAINLIEST
Answer:
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If an article costs a store $17.45 and if it sells the article for $22.95, what percentage markup is it using?L
4[1 2 -1 5]
Someone help me with this bs
Answer:
-12
Step-by-step explanation:
12 - 15 = -3
4 ( -3 )
= -12
Answer: -12
Step-by-step explanation:
We have 4[12 -15]
Next, we have subtract in the parentheses since it's part of PEDMAS
12-15
After that, we get -3. Whenever a you multiply a whole number with a negative number, the whole becomes negative.
12- 15= -3
And Lastly, we multiply.
4x -3= -12
Hope this helps!
Determine whether the line through (−4, 7) and (−2, −1) intersects the line through (−3, −3) and (−1, −7).
Answer:
no it does not
Step-by-step explanation:
[8-(-12)]÷(2x-2)-(-8)
Answer:
3
Step-by-step explanation:
find the circumference of the circle below use 3.14 for
Answer:
31.4
Step-by-step explanation:
R= 5
2 x 3.14 x 5= 31.4
Find the diameter of the circle below round to the nearest hundredth
Answer:
Step-by-step explanation:
[tex]C=2\pi r=\pi d\\ \\ d=\frac{C}{\pi}, C=15\\ \\ d=frac{15}{\pi}\\ \\ d\approx 4.77yds[/tex]
2nd time asking! I need answer please.
Answer:
33.49 cubic centimeters
Step-by-step explanation:
Equation for volume: 4/3*π*r^3
Substitute 2 for r and 3.14 for π
4/3*3.14*2^3
To the nearest hundredth is 33.49
which choice are equivalent to the fraction below? check all apply.
30/90
A. 15/45
B. 2/3
C. 1/3
D. 6/12
E. 20/40
F. 5/15
Answer:
Ans = 1/3
Step-by-step explanation:
30/90 divide by 10 equals 3/9
3/9 divide by 3 equals 1/3
3 Xavier sketches several designs for a math club
Concept Application
pin. The math club voted for the pin shape to
be a right triangle. Which of the following
triangles could NOT be the shape used for the
math club pin?
13
17
А
12
15
26
D
24
12
Answer:
D ...
Step-by-step explanation:
Use the Pythagorean Theorem to figure out which triangle is NOT a right triangle. Square each leg and add them together. Then, square the hypotenuse (longest side). If the sums are equal, then the triangle IS a right triangle.
Pythagorean Theorem:
a(a) + b(b) = c(c) ; a squared plus b squared equals c squared
6(6) + 24(24) =? 26(26) ; leg a =6, leg b=24, hypotenuse=26
36 + 576 =? 676 ; simplify
612 =? 676 ; is 612 equal to 676?
solving to find t
|17t + 8| + 7 = 10
Answer:
t1= -11/17, t2=-5/7
Step-by-step explanation:
i think this is what you were looking for...