Answer:
Step-by-step explanation:
A) y = -20x + 2500
The above equation is written in slope intercept form - y=mx+b - the y int. is 2500, while the rate of change, aka the slope, is -20 feet per minute.
B) (0,2500) (1,2480) (2,2460) (3,2440) (4,2420)
For this question just plug in the x values 0 to 4 into the equation above. For example -20(0) +2500 = 2500
C) 1700 feet above the ground
Plug the number 40 into the equation above. -20(40) + 2500 = 1700
D) 125 minutes
The y-int. represents the time it takes him to reach the ground, this means you can set the equation equal to zero and solve to find the answer.
0 = -20x + 2500
subtract 2500 from both sides
-2500 = -20x
divide -20 from both sides
125 = x
Answer:50m
Step-by-step explanation: the highest
I keep gettin this wrong please help!!!
Answer:
Slow = 30
Fast = 50
Step-by-step explanation:
So make variables for the speed.
Slow wanderer = x
Faster wanderer = x + 20
The time it took was 2.5 hours.
2.5x + 2.5x + 50 = 200
5x + 50 = 200
x = 30
What’s the correct answer for this?
Answer:
36
Step-by-step explanation:
Diameter AB bisects the chord
MO = NO
5x+3=6x
3 = 6x-5x
x = 3
Now
MN = 5x+3+6x
MN = 5(3)+3+6(3)
MN = 15+3+18
MN = 36
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
290
Step-by-step explanation:
(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. ModifyingBelow Integral from nothing to nothing With Upper C (y minus z )ds∫C(y−z)ds; C is the helix left angle 12 cosine t comma 12 sine t comma t right angle12cost,12sint,t, for 0 less than or equals t less than or equals 2 pi0≤t≤2π The value of the ordinary integral is nothing.
C is parameterized by
[tex]\vec r(t)=\langle x(t),y(t),z(t)\rangle=\left\langle12\cos t,12\sin t,t\right\rangle[/tex]
for 0 ≤ t ≤ 2π. In the integral, replace y and z as above, and the line element ds is
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{145}\,\mathrm dt[/tex]
So the integral is
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=\sqrt{145}\int_0^{2\pi}(12\sin t-t)\,\mathrm dt[/tex]
sin(t) has period 2π, so that term contributes nothing to the integral, leaving us with
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=-\sqrt{145}\int_0^{2\pi}t\,\mathrm dt=\boxed{-2\pi^2\sqrt{145}}[/tex]
Two models R1 and R2 are given for revenue (in billions of dollars per year) for a large corporation. The model R1 gives projected annual revenues from 2008 through 2015, with t = 8 corresponding to 2008, and R2 gives projected revenues if there is a decrease in the rate of growth of corporate sales over the period. Approximate the total reduction in revenue if corporate sales are actually closer to the model R2. (Round your answer to three decimal places.) R1 = 7.21 + 0.55t R2 = 7.21 + 0.44t
Answer:
7.0422 is the correct answer to the given question .
Step-by-step explanation:
Given
R1 = 7.21 + 0.55t
R2 = 7.21 + 0.44t
Decrease in the revenue can be determined by the formula
[tex]= Reduction\ in\ R1\ -\ Reduction\ in\ R2[/tex]
[tex]= (7.21 + 0.55t ) - (7.21 + 0.44t)[/tex]
=0.11 t
Now overall Reduction can be determined by the interval from t=8 to t=15
Consider c=0.11 t
[tex]\frac{dc}{dt}[/tex]=0.11
Now integrated the equation from t=8 to t=15 to determine total reduction in revenue
[tex]=\int_{8}^{15}\sqrt{1+0.11^2}\ dL[/tex]
[tex]=7.0422[/tex]
A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 14 in. beyond its natural length? W = ft-lb
Answer:
The work done in stretching it from its natural length to 14 in. beyond its natural length is W=8.17 ft-lb.
Step-by-step explanation:
We know that a force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length.
This let us calculate the spring constant k as:
[tex]F=kx\\\\k=F/x=(8 \;lb)/(8\;in)=1\;lb/in[/tex]
We know that work is, in an scalar form, the product of force and distance.
The force F is equal to the spring constant multiplied by the distance from the natural length.
Then, as the force changes with the distance from the natural length, we have to calculate integrating:
[tex]W=\int_0^{14}F\,dx=\int_0^{14}kx\,dx\\\\\\W=\dfrac{1}{2}kx^2\left|^{14}_0=\dfrac{1}{2}(1\,lb/in)(14 \,in)^2-\dfrac{1}{2}(1\,lb/in)(0 \,in)^2[/tex]
[tex]W=98lb\cdot in-0lb-in\\\\W=98(lb\cdot in)\cdot \dfrac{1 \,ft}{12\,in}=8.17\;lb\cdot ft[/tex]
Y is directly proportional to (x+2)2 when x=8 y = 250 find y when x=4
Answer: 150
Step-by-step explanation: K is constant
250= K (8+2)2
250= K (10)2
250= K (20)
250= K20
divide both sides by 20
250/20= K
12.5= K
THEREFORE
Y= K (4+2)2
Y= 12.5 (6)2
Y= 12.5 × 12
Y= 150
At x = 4 the value of the variable y will be 90 as per the proportionality given.
What is proportionality?The property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, Y is directly proportional to (x+2)2 when x=8 y = 250
Since Y ∝ (x + 2)²
Y = k (x + 2)²
Where k is constant
For x = 8 y = 250
Substituting the values
250 = k(8 + 2)²
k = 2.5
Thus for x= 4
y = 2.5 (4 + 2)²
y = 90
therefore, According to the proportionality, the variable y will have a value of 90 at x = 4.
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f(x)=2x-6 g(x)=3x+9, find (f+g)
Answer:
(f+g)(x) = 5x +3
Step-by-step explanation:
(f+g)(x) = f(x) +g(x)
= (2x -6) +(3x +9)
= 2x +3x -6 +9
(f+g)(x) = 5x +3
Question 20 (5 points)
In a jet engine, what purpose does the afterburner serve?
A,) It reheats the gas from the fuel and releases it more rapidly.
B.) It burns fuel once the plane reaches its maximum altitude.
C.) After the plane lands, it burns off excess fuel that wasn't used in flight.
D.) It provides a way to slow the plane down by cooling the exhaust gas.
It reheats the gas from the fuel and releases it more rapidly.
The answer is option A.
How long can a jet fly on an afterburner?In full afterburner at low altitudes, the F-16 can burn in excess of 64,000 pounds an hour. At full throttle, a U.S.-variant F-16 with maximum external fuel stores has about 20 minutes until it's on emergency reserves (which would only last an extra minute or so at full afterburner).
Does afterburner increase thermal efficiency?Since the exhaust gas already has a reduced oxygen content, owing to the previous combustion, and since the fuel is not burning in a highly compressed air column, the afterburner is generally inefficient in comparison to the main combustion process.
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Terry, Edin and Gordon are hygiene inspectors. Three takeaways, kebab, fish and chips and pizza. It is decided to share the work so that all inspectors will visit one takeaway each, chosen at random. List all the possible different ways they could share the work. (TK-EF-GP,
Answer: There are 6 different ways in which they can share the work.
Step-by-step explanation:
Suppose that Terry selects first the place where he goes, in the selection he has 3 options at random to chose.
Then Edin selects, Edin has two options (because one is already taken)
Then Gordon selects, he has only one options.
The number of combinations is equal to the product of the number of options for each selection, this is:
Combinations = 3*2*1 = 6
There are 6 different ways in which they can share the work.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Circle with centre (0,2) will have the equation
(x)²+(y-2)² = r²
Finding r² by distance formula using P(-7,2)
r² = (-7-0)²+(2-2)²
r² = (-7)²
r² = 49
So substituting in the equation
x²+(y-2)² = 49
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final values of the stock, then:______A) A = B = CB) A = B < CC) C < B = AD) A < B < CE) B < A < C
Answer:
E) B < A < C
Step-by-step explanation:
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.
Initial Values are: A, B and C
After one year, A was up 20%, B was down 25%, and C was unchanged.
Values after one year:
A=(100%+20%) of $100=$120 worth of stock.B=(100-25%) of $100=$75 worth of stock.C=100% of $100=$100 worth of stock.For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.
Values after the second year
A=(100%-20%) of $120 =80% of $120=$96 worth of stock.B=(100%+25%) of $75 =125% of $75=$93.75 worth of stock.C=100% of $100 =$100 worth of stock.Therefore, from the final values of the stock, we have that:
B<A<C
The correct option is E.
5x + 6y = 32
5x – 6y = 8
Which variable or variables will be eliminated when you add the system of equations?
Answer:
The variable y is eliminated.
Step-by-step explanation:
To add a system of equations, we add the common terms. x with x, y with y and values with values.
In this question:
5x + 6y = 32
5x – 6y = 8
Adding:
5x + 5x + 6y - 6y = 32 + 8
10x = 40
So the variable y is eliminated.
Answer:
10x 40
Step-by-step explanation:
Lines sand tare perpendicular. If the slope of line sis 5, what is the slope of
line t?
Answer:
-1/5
Step-by-step explanation:
Perpendicular lines have slopes that are the opposite reciprocal of one another.
The slope of line t is the opposite reciprocal of the slope of line s:
slope of t = -1/(slope of s)
slope of t = -1/5
what’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
98%
The probability of not winning the raffle is 100% - 2% = 98%
The sum of a number and its reciprocal is 41/20. Find the number. smaller value larger value
Step-by-step explanation:
Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :
[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]
It is a quadratic equation. The values of x are :
[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]
The smaller number is 4/5 and the larger number is 5/4.
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
C.
Step-by-step explanation:
Some rectangles can be squares, since they fit the criteria for both if it is a square, but not ALL rectangles can be squares, since squares have ALL 4 sides congruent, whereas rectangles only have 2 sets of sides congruent.
How many edges dose the following shape have?
Given the data shown below, which of the following is the best prediction for
the number of years it will take for the population to reach 200,000?
Year
Population
11,920
2
16,800
3
23,300
4
33,000
5
45,750
6
64,000
O A. 9.41
O B. 12.45
O C. 15.82
O D. 18.14
Answer:
The best prediction for the number of years it will take for the population to reach 200,000 is 9.41
Step-by-step explanation:
Year Population
1 11,920
2 16,800
3 23,300
4 33,000
5 45,750
6 64,000
[tex]y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)[/tex]
Substitute the values
[tex]11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2[/tex]
Divide 1 and 2
[tex]\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238[/tex]
The exponential function that passes through the points (1, 11920) and (2, 16800) is[tex]y=8457.5238 e^{0.3432t}[/tex]
Now we are supposed to find the best prediction for the number of years it will take for the population to reach 200,000
[tex]200000=8457.5238 e^{0.3432t}[/tex]
[tex]\frac{200000}{8457.5238}=e^{0.3432t}[/tex]
[tex]ln(\frac{200000}{8457.5238})=0.3432t[/tex]
t = 9.41
Hence the best prediction for the number of years it will take for the population to reach 200,000 is 9.41
What is this answer?
Answer:
1
Step-by-step explanation:
coz 1 x 1 x 1=1
Trey is estimating the length of a room in his house. The actual length of the room is 17 m. Trey's estimate is 15 m.
Find the absolute error and the percent error of Trey's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Absolute error = 2m
Step-by-step explanation:
Absolute Error = Measured Value - Actual Value
17m - 15m = 2m
Answer:
2m and 11.8%
Step-by-step explanation:
Absolute error is defined mathematically as;
Error/original value
[Original value - estimated value]
[17-15 ] = 2m
The percentage error would be
[Original value - estimated value]/ original value
[17-15 ] /17 × 100%
0.1176 × 100% = 11.76%
11.8%[ to the nearest tenth]
Find the largest prime factor of 309^2 - 147^2.
Answer: 2^4*3^5*19
Step-by-step explanation:
You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.
The largest prime factor of 309² - 147² is, 19.
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is,
⇒ 309² - 147²
Now, We can simplify as;
⇒ 309² - 147²
⇒ (309 - 147) (309 + 147)
⇒ 162 × 456
⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19
Thus, The largest prime factor of 309² - 147² is,
⇒ 19
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The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses: 4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1 11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5 7.5 6.2 5.8 2.7 3.4 10.4 9.8 6.6 3.7 6.4 8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.2 6.2 5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3 7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.1 7.2 5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2 8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7 5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6 10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6 7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3 9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2 8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Answer:
Step-by-step explanation:
For n=129 and with leaf unit = 0.1, the stem and leaf chart of the given data on Shower-flow rate (L/min) is as follows:
2 28
Stem leaves
3----------1344567789
4----------01356889
5----------00001114455666789
6----------0000122223344456667789999
7----------00012233455555668
8----------02233448
9----------012233335666788
10----------2344455688
11--------- 2335999
12---------- 17
13-------- 9
14--------36
15---------- 0035
16---------None
17---------None
18 ----------3
* From steam and leaf chart we note that minimum Shower flow rate is 2.2 whereas maximum is 18.3 L/mim. Further typical or representative rate is 7.0 L/min.
* The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.
* Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.
* From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.
A cellular phone network uses towers to transit calls. Each tower transmits a circular area. on a grid of a city, the equations given represent the transmission boundaries of the towers. Tell which towers, is any, transmit to a phone located at M(3.5, 4.5).
Tower A: x^2 + y^2 = 9
Tower B: (x - 5)^2 + (y - 3)^2 = 6.25
Tower C: (x - 2)^2 + (y - 5)^2 = 4
Answer:
B
Step-by-step explanation:
Notice that
[tex](3.5-5)^2 + (4.5-3)^2 = 4.5[/tex]
Since 4.5 is less than 6.25, tower B transmits to that phone
Answer:
Towers B and C transmit to the phone.
Step-by-step explanation:
First, let see the location of the center for each tower:
Tower A
[tex]A (x,y) = (0,0)[/tex]
Tower B
[tex]B (x,y) = (5,3)[/tex]
Tower C
[tex]C(x,y) = (2,5)[/tex]
Now, the distance between the location of the phone and any of the towers by means of the Pythagorean equation. The phone is under the influence of a tower only if distance is less than transmission boundaries. Then:
Tower A
[tex]d_{A} = \sqrt{(3.5-0)^{2}+(4.5-0)^{2}}[/tex]
[tex]d_{A} \approx 5.701[/tex]
[tex]d_{A} > 3[/tex]
Tower B
[tex]d_{B} = \sqrt{(3.5-5)^{2}+(4.5-3)^{2}}[/tex]
[tex]d_{B} \approx 2.121[/tex]
[tex]d_{B} < 2.5[/tex]
Tower C
[tex]d_{C} = \sqrt{(3.5-2)^{2}+(4.5-5)^{2}}[/tex]
[tex]d_{C} \approx 1.581[/tex]
[tex]d_{C} < 2[/tex]
Towers B and C transmit to the phone.
A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample space first.]
Answer:
[tex]p = \frac{4}{9}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Sample space:
All posible outcomes.
First answer - Second answer:
A - A
A - B
A - C
B - A
B - B
B - C
C - A
C - B
C - C
9 possible outcomes.
Probability that neither is B.
A - A
A - C
C - A
C - C
4 possible outcomes.
So
[tex]p = \frac{4}{9}[/tex]
expand and simplify (4+√2)(6-√2)
Answer:
[tex]22+2\sqrt{2}[/tex]
Step-by-step explanation:
[tex](4+\sqrt{2} )(6-\sqrt{2} )[/tex]
[tex]4(6)-4\sqrt{2} +6\sqrt{2} -2[/tex]
[tex]24+2\sqrt{2} -2[/tex]
[tex]22+2\sqrt{2}[/tex]
A sports-equipment factory produces sports balls. On Monday, they produced 1,080 balls altogether. All of the balls they produced were either volleyballs or soccer balls. They produced 7 times as many volleyballs as soccer balls. How many soccer balls did the factory produce on Monday?
Answer: 135 soccer balls
Step-by-step explanation:
In this equation, let x represent the number of soccer balls, and 7x represent the number of volley balls.
7x + x = 1,080
8x = 1,080
Now divide 1,080 by 8 to get the number of soccer balls.
1,080 / 8 = 135
In case you’re wondering how to find the number of volley balls, just multiply 135 by 7
135 * 7 = 945
An old saying in golf is "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour's world money list are examined. The average number of putts per hole and the player's total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software. the p-value for the test in question 3 is 0.0087. p-value for the test in question 3 is 0.0087. a correct interpretation of this result is that:____________
Answer:
With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.
Step-by-step explanation:
In this case, the hypothesis test has the following hypothesis:
Null hypothesis: there is no relationship between the average number of putts per hole and the player's total winnings.
Alternative hypothesis: there is relationship between the average number of putts per hole and the player's total winnings.
Then, a P-value of 0.0087 is, without doubt, a strong evidence that the null hypothesis is false.
With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.
81. Restaurants. About 12% of the restaurants in the US are pizzerias, and there are about 70,000 pizzerias in the US. Estimate the total number of restaurants in the United States.
Answer:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
Step-by-step explanation:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?
Answer:
Step-by-step explanation:
Given that
n = 25
mean = 3100
standard deviation = 500
[tex]\bar x = \frac{500}{\sqrt{25} }[/tex]
= 500 / 5
= 100
N ( μ = 3500, (500)² / 25)
N = (3500,(100)² )
b) P ( x < 3100)
c) Z score
[tex]z = \frac{x - u _{\bar x}}{\sigma \_ {\bar x}}[/tex]
[tex]u_{\bar x}= 3500[/tex]
[tex]\sigma _{\bar x}= 100[/tex]
[tex]z = \frac{3100-3500}{100} \\\\= -4[/tex]
d)
probability=
P ( x < 3100) = P < -4 = 0
Answer:
a) The parameters for the sampling distribution include
Mean = μₓ = 3500 g
Standard deviation = σₓ = 100 g
Required probability = P(x < 3100)
b) The image of the probability density curve is presented in the attached image.
c) The z-score for 3100 g in the sampling distribution = -4.00
d) The probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003
Step-by-step explanation:
Complete Question
Suppose we know the birth weights of babies is normally distributed, with mean of 3500 g and standard deviation 500g.
If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?
a) What are the parameters?
b) Draw a probability density curve for the problem.
c) What is the z-score of the weight?
d) What is the required probability?
Solution
The Central limit theorem explains that for a random sample of adequate size obtained from a normal distribution with independent variables, the mean of the sampling distribution is approximately equal to the population mean and the sampling distribution is approximately of the nature of the population distribution (normal) with the standard deviation of the sampling distribution given as
Standard deviation of the sampling distribution = [(Population Standard deviation)/√n]
σₓ = (σ/√n)
Mean of Sampling distribution = Population mean
μₓ = μ = 3500 g
σₓ = (σ/√n) = (500/√25) = 100 g
a) The parameters for the sampling distribution include
Mean = μₓ = 3500 g
Standard deviation = σₓ = 100 g
Required probability = P(x < 3100)
b) The image of the probability density curve is presented in the attached image.
c and d) To obtain the required probability, we need the z-score for 3100 g, so we standardize 3100g
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (3100 - 3500)/100 = - 4.00
To determine the required probability 45mg/L, P(x < 3100) = P(z < -4.00)
We'll use data from the normal probability table for these probabilities
P(x < 3100) = P(z < -4.00) = 0.00003
Hence, the probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003
Hope this Helps!!!!