Answer:
6781632 ft ^ 3
Step-by-step explanation:
The first thing is to know the formula for the volume of a pyramid:
V = 1/3 * Ab * h
That is, it is one third of the product between the area of the base and the height.
The base area would be:
Ab = l ^ 2
the side equals 156 ft, replacing:
Ab = 156 ^ 2
Ab = 24336 ft ^ 2
now, replacing in the volume formula:
V = 1/3 * 24336 * 836
V = 6781632
Which means that the volume of the pyramid is 6781632 ft ^ 3
Henry, Brian and Colin share some sweets in the ratio 6:4:1. Henry gets 25 more sweets than Colin. How many sweets are there altogether?
Answer:
There are 55 sweets in total.
Step-by-step explanation:
The total number of sweets is t.
Henry, Brian and Colin share some sweets in the ratio 6:4:1.
This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).
Brian earns [tex]\frac{4}{11}[/tex] of the total.
Colin earns [tex]\frac{1}{11}[/tex] of the total
Henry gets 25 more sweets than Colin.
Henry earns [tex]\frac{6t}{11}[/tex]
Colin earns [tex]\frac{t}{11}[/tex]
So
[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]
Multiplying everything by 1
[tex]6t = t + 275[/tex]
[tex]5t = 275[/tex]
[tex]t = \frac{275}{5}[/tex]
[tex]t = 55[/tex]
There are 55 sweets in total.
Watermelon A is 2 kg lighter than watermelon B and it weighs one fifth of the weight of watermelon C. Watermelons A and C together are 3 times as heavy as watermelon B. How heavy is each watermelon?
Answer:
A: 2 kgB: 4 kgC: 10 kgStep-by-step explanation:
We can write some equations to describe the given relationships:
A = B - 2 . . . . . A is 2 kg lighter than B
A = C/5 . . . . . . A is 1/5 the weight of C
A+C = 3B . . . . together, A and C are 3 times the weight of B
__
Let's solve for A.
B = A+2 . . . from the first equation
C = 5A . . . . from the second equation
A +5A = 3(A+2) . . . . substituting for B and C in the third equation
6A = 3A +6
3A = 6
A = 2
__
B = A+2 = 4
C = 5A = 10
Watermelon A weighs 2 kg; B weighs 4 kg; and C weighs 10 kg.
Answer:
2 kg 4 kg 10 kg
I BLESS THE EYES!
The differential equation below models the temperature of a 91°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. dy dt = − 1 53 (y − 17)\
Answer:
[tex]t \approx 17.690\,min[/tex]
Step-by-step explanation:
This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:
[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]
[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]
[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]
[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]
[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]
The solution of the differential equation is:
[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]
Where:
[tex]y[/tex] - Temperature, measured in °C.
[tex]t[/tex] - Time, measured in minutes.
The time when the cup of coffee has the temperature of 70 °C is:
[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]
[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]
[tex]t \approx 17.690\,min[/tex]
How do u solve this?
Answer:
0
Step-by-step explanation:
Tuesday : -1/2
Wednesday + 3/4
Thursday : -3/8
Add them together
-1/2 + 3/4- 3/8
Get a common denominator
-4/8 + 6/8 - 3/8
-1/8
The closest integer value to -1/8 is 0
Please answer this correctly
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
Tameka can make 32 beads with 4 sheets of paper. Right now she only has 3 sheets of paper. How many beads can Tameka make?
Answer:
24 beads
Step-by-step explanation:
beads in 4 sheet=32
beads in 1 sheet=32/4=8
beads in 3 sheet=8*3=24
Answer:
Assuming that you can make the same number of beads with 1 sheet of paper, Tameka can make 24 beads with 3 sheets of paper.
Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such sunflower seeds is randomly selected. The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
Answer:
12.08
Step-by-step explanation:
For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Seventy-six percent of sunflower seeds will germinate into a flower
This means that [tex]p = 0.76[/tex]
Samples of 800:
This means that [tex]n = 800[/tex]
The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]
For which x is f(x)?=-3
-7
-4
4
5
Answer:
B.
✔ -4
Step-by-step explanation:
E 2021
A soccer field is a rectangle 30 meters wide and 120 meters long.The coach asks players to run from one corner to the corner diagonally across. What is the distance to the nearest tenth of a mile
Answer:
123.7 meters
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 30. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
30^2 + 120^2 = c^2
c=123.7
please help me explain your answer only answer if you are sure
Answer:
The answer of top prism is 262
and down prism is 478
The upper figure is triangular prism.
so, we use bh+2ls+lb formula
B=5
h=3
s=4
l=19
Now,
surface area of triangular prism = bh+2ls+lb
= 5×3+2×19×4+19×5
= 262
The down figure is rectangular prism.
so, we use 2lw+2lh+2hw
l=5
h=6
w=19
Now,
The area of rectangular prism = 2lw+2lh+2hw
= 2×5×19+2×19×6+2×5×6
= 478
Look at the work shown for the division problem shown on the right. The remainder is 8 . Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2. f (–2) = 8 Compare the values you entered above. f (–2) is the remainder when dividing the polynomial by x + 2. Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.
Answer:
1st : 8
2nd: 8
3rd: equal to
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
The remainder of the polynomial when divided by x + 2 is -60.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 divide by x + 2.
Now,
x + 3 ) 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 ( 2x³ - 2x² - 5x + 18
2[tex]x^{4}[/tex] + 6x³
(-) (-)
-2x³ - 11x² + 3x - 6
-2x³ - 6x²
(+) (+)
- 5x² + 3x - 6
-5x² - 15x
(+) (+)
18x - 6
18x + 54
(-) (-)
-60
We see that,
The remainder is -60.
f(-2) = 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6
f(-2) = 2 x 16 + 32 - 44 - 6 - 6 = 32 + 32 - 44 - 12 = 64 - 56 = 8
Thus,
The remainder of the polynomial when divided by x + 2 is -60.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ2
Two positive numbers have a difference of 8. The larger number is three more than twice the smaller. Find the two numbers.
Answer:
5 and 13
Step-by-step explanation:
Let x represent the smaller number. Then the larger number is 2x+3, and the difference is ...
(2x+3) -(x) = 8
x = 5
The two numbers are 5 and 13.
_____
Check
Twice the smaller number is 10. 3 more than that is 13, the larger number. Their difference is 13 -5 = 8.
A gumball machine has 100 red gumballs. If the red gumballs are 25% of the total number of gumballs, how many gumballs are in the gumball machine?
Answer: 400
Step-by-step explanation:
25% is equal to one quarter (1/4). If theres 100 red gumballs then there must be 300 more gumballs in the machine because a quarter of a number is always even.
22,056 people went to the baseball game on Sunday. Half as many people came on money. How many people were at the baseball game on Sunday and Monday altogether?
Answer:
33084
Step-by-step explanation:
22056 divided by 2 =11028
altogether (on sunday and monday) the total amount would be..
22056+11028=33084
Answer:
33084
Step-by-step explanation:
If 22056 people came to the game on Sunday and Half as many people came on Monday, you do
22056 divided by 2. this is how many people cam on monday
Add this answer to 22056 and this is how many people came on both days.
A bag contains 1p,20 and 5p coins 3/8 of the bag are 1p coins There are as many 5p coins as 1p coins in the bag. There are 640 coins in total. Work out the number of 20 coins in the bag
Answer:
160 off 20p coins
Step-by-step explanation:
1 p, 20 p, 5 p coins1 p= 3/8 of the bag5 p= 1 p= 3/8 of the bagtotal coins= 64020 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160
Temperature transducers of certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:
2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 41 2 3 2 2 8 4 5 1 3 1
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 2 3
a. Determine frequencies and relative frequencies for the observed values of x = number of non-conforming transducers in a batch. (Round your relative frequencies to three decimal places.)
b. What proportion of batches in the sample have at most four non-conforming transducers? (Round your answer to three decimal places.)
Answer:
a.
Number: 0, 1, 2, 3, 4, 5, 6, 7, 8
Frequency: 6, 12, 13, 15, 5, 3, 3, 1, 1
b. The proportion of the batches that have at most is 0.864
Step-by-step explanation:
a. The given data are;
2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 2 3
The frequencies are;
x fx
0 6
1 12
2 13
3 15
4 5
5 3
6 3
7 1
8 1
The relative frequency are;
x Rfx
0 0.102
1 0.203
2 0.220
3 0.254
4 0.085
5 0.051
6 0.051
7 0.017
8 0.017
b. The proportion of the batches that have at most 4 is given as follows;
The number of the batches that have at most 4 = 6 + 12 + 13 + 15 + 5 = 51
Therefore, the proportion of the batches that have at most 4 = 51 / 59 = 0.864.
Help Me PLEASE!!!
A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?
Answer:
P = 0.5207
Step-by-step explanation:
First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.
Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).
So, the probability that just the first card is a diamond or an ace is calculated as:
[tex]P_1=\frac{16}{52}*\frac{36}{52}=0.2130[/tex]
At the same way, the probability that just the second card is a diamond or an ace is:
[tex]P_2=\frac{36}{52}*\frac{16}{52}=0.2130[/tex]
Finally, the probability that both cards are diamonds or aces is:
[tex]P_3=\frac{16}{52}*\frac{16}{52}=0.0947[/tex]
Therefore, the probability that at least one of the cards is a diamond or an ace is:
[tex]P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207[/tex]
Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
PROOF:
[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
6(4x - 3) - 30
24x - 18 = 30
24% -18 + 18 = 30 + 18
24x = 48
24x 48
24 24
X = 2
Original Equation
Step 1
Step 2
Step 3
Step 4
Step 5
Which of these is not part of the solution process?
A. Using the associative property
B. Adding 18 to both sides to isolate the variable term
C. Dividing both sides by 24 to isolate the variable
D. Using the distributive property
Answer:
A-using the associative property
Step-by-step explanation:
36°
I
80°
w
m
What equation can be used to calculate the measure of angle ? Describe, in words, the
process you would use to find
Answer:
44°
Step-by-step explanation:
A pair of angles formed from the intersection of two lines opposite to each other at the point of intersection (vertex) is called vertically opposite angles. These vertically opposite angles are congruent to each other (that means they are equal).
Since opposite angles are equal, the equation needed to calculate w is given as:
80° = 36° + w
w = 80° - 36°
w = 44°
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone. What probability distribution describes this situation and what are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
Answer:
We use the binomial distribution to describe this situation.
The mean number of phone sales is 749.7 with a standard deviation of 15.
Step-by-step explanation:
For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
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]
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.
This means that [tex]p = \frac{35}{50} = 0.7[/tex]
What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
1071 shoppers, so [tex]n = 1071[/tex]
Mean
[tex]E(X) = 1071*0.7 = 749.7[/tex]
Standard deviation
[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]
The mean number of phone sales is 749.7 with a standard deviation of 15.
Devon wants to build a ramp with the dimensions shown. How much wood does he need?
The image of the ramp with dimensions is missing, so i have attached it.
Answer:
680 in² of wood is needed.
Step-by-step explanation:
The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.
From the attached image,
Let's find the area of the 2 triangles first;
A1 = 2(½bh) = bh = 15 x 8 = 120 in²
Area of the slant rectangular portion;
A2 = 17 x 14 = 238 in²
Area of the base;
A3 = 15 × 14 = 210 in²
Area of vertical rectangle;
A4 = 8 × 14 = 112 in²
Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²
Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p= 0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of guesses made for the sat questions.
Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2
Probability of failure, q = 1 - p = 1 - 0.2 = 0.8
the probability that the number x of correct answers is fewer than 4 is expressed as
P(x < 4)
From the binomial distribution calculator,
P(x < 4) = 0.97
HELP ME QUICK!! The best answer I will mark brainlest!
Answer: 1. (4, 8); 2. (3, 4)
Step-by-step explanation: I tried to get this to you fast but I can give you an explaination if you would like one :)
What is a word problem for 15 minus 28?
Answer:
A word problem for that would be Sam had 28 chocolates and Bob took away 15. How many does Sam have left?
Step-by-step explanation:
I don't know how to show work for writing a word problem. Sorry
Answer:
Step-by-step explanation:
Jane has $15 in her bank account. She wrote a $28 check for buying a fiction book. How much is her balance now?
What’s the correct answer for this question?
Answer:
A: 97π/18 m
Step-by-step explanation:
Central Angle = 97°
In radians:
97° = 97π/180
Now
S = r∅
S = (10)(97π/180)
S = 97π/18 m
Answer:
The answer is option 1.
Step-by-step explanation:
Given that the formula for length of Arc is Arc = θ/360×2×π×r when r represents the radius of circle. Then, you have to substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
Let θ = ∠VCW = 97°,
Let r = 10m,
[tex]arc = \frac{97}{360} \times 2 \times \pi \times 10[/tex]
[tex]arc = \frac{97}{360} \times 20 \times \pi[/tex]
[tex]arc = \frac{97}{18} \pi \: m[/tex]
The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2.
Required:
a. Estimate at 5% level of significance whether the true average shrinkage percentage U: is greater than 17.5 and write your conclusion.
b. Report the p-value.
Answer:
a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
Part b
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Write a quadratic function f whose zeros are −6 and −1.
Answer:
y = (x+6) (x+1) or in quadratic form: y = x² + 7x + 6
Step-by-step explanation:
2. En la ciudad de Quito, en la temporada fría, se registran temperaturas que van desde los 5 °C hasta los 18 °C. En la temporada cálida, el registro de la temperatura va desde los 4 °C hasta los 30 °C.
a. Representamos estas temperaturas en forma de intervalo y como conjunto.
b. ¿A qué intervalo pertenece la temperatura de la ciudad de Quito?
c. ¿Qué temperaturas son comunes en las temporadas fría y cálida?
d. ¿Qué temperaturas son posibles solo en la temporada fría?
e. ¿Qué temperaturas son posibles solo en la temporada cálida?
Answer:
(See explanation below for further detail/Véase la explicación abajo para mayores detalles)
Step-by-step explanation:
(This exercise is written in Spanish and explanations will be held in such language)
a) Las temperaturas quedan representadas a continuación:
Quito - Temporada Fría
Intervalo
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)
Conjunto
[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)
Quito - Temporada Cálida
Intervalo
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)
Conjunto
[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)
b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:
Intervalo de Temporada Fría:
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]
Intervalo de Temporada Cálida:
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]
c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.
d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.
e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.
New York City is known for it's tourist attractions and high priced real estate. The mean hotel room rate is $202 per night. Assume that the room rates are normally distributed with a standard deviation of $70.What is the probability that a hotel room costs between $210 and $290?
Answer:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
Step-by-step explanation:
Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(202,70)[/tex]
Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]
We are interested on this probability
[tex]P(210<X<290)[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the formula we got:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
