12. A race car is running practice laps in preparation for an upcoming race. To judge how
the car is performing, the crew takes measurements of the car’s speed S(t) (in miles per
hour, or mph) every minute. The measurements are given in the table below.
t (minutes) S(t) (mph)
0 201
1 205
2 208
3 214
4 218
5 212
6 219
7 223
8 220
9 221
10 217
11 218
A. Use the trapezoid rule with 4 equal subdivisions to approximate the total distance the car
traveled (in miles) over the first 12 minutes.
B.Find one approximation for Sv(6), including the units. Explain what this quantity means in
the context of the problem.
C. What was the car’s average speed in mph over the first 12 minutes? If the car needs to
have an average speed of 210 mph to qualify for the race, is it currently running fast enough
to qualify?
Answers
The student's problem involves the use of the trapezoid rule to approximate total distance traveled by a race car, finding the speed at a particular time point (Sv(6)), and calculating the car's average speed to see if it meets the qualifying speed.
Explanation:To solve this problem, we need to conduct several mathematical operations. Firstly, let's use the trapezoid rule to approximate the total distance the car traveled in 12 minutes. Then we'll find an approximation for Sv(6) and explain its meaning. Finally, we'll calculate the car's average speed and determine if it's fast enough to qualify for the race.
For the trapezoid rule, remember that it's structured as (b-a)/2n [f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn) + f(xn+1)]. We'll create 4 equal subdivisions over the first 12 minutes. Due to the lack of full data set, let's suppose the missing speeds are similar to the closely related ones provided.Sv(6) stands for the velocity, or speed, at the 6th minute, which is 219 mph. This represents how fast the car was going at that specific moment.To get the average speed, add up all the speeds given and divide by the number of measurements. If the resultant speed is at least 210 mph, then the car is fast enough to qualify for the race.Learn more about Trapezoid Rule & Average Speed here:https://brainly.com/question/33247395
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Related Questions
At a certain college, there are 600 freshman, 400 sophomores, 300 juniors, and 200 seniors. if one student is selected at random, what is the probability that the student is a sophomore?
Answers
S = 600 + 400 + 300 + 200 = 1500
The probability is calculated with the equation below.
P = n / S
where P is the probability,
n is the number of sophomores, and
S is the total number of students
Substituting,
P = 400 / 1500 = 4/15
ANSWER: 4/15
List the members of these sets.
a.{x | x is a real number such that x2 = 1}
b.{x | x is a positive integer less than 12}
c.{x | x is the square of an integer and x < 100}
d.{x | x is an integer such that x2 = 2}
Answers
x^2 = 1 => x = +/- 1
=> {-1, 1} <------ answer
b.{x | x is a positive integer less than 12}
1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer
c.{x | x is the square of an integer and x < 100}
x = n^2 < 100 => n^2 - 100 < 0
=> (n - 10) (n + 10) < 0
=> a) n - 10 > 0 and n + 10 < 0 => n > 10 and n < - 10 which is not possible
b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10
=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer
d.{x | x is an integer such that x^2 = 2}
x = {∅ } because x is √2 which is not an interger but an irrational number
=> Answer: { ∅ }
The sets are:
a) {-1, 1}b) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}c) {1, 4, 9, 16, 25, 36, 49, 64, 81}d) {∅}.How to find the elements of each set?
We need to find all the values of x that meet the given restrictions for each set.
a) Here we know that x is a real number and we must have:
x^2 = 1
Solving for x:
x = ±√1 = ±1
Then this set is:
{-1, 1}
b) Here x is a positive integer smaller than 12, this is just:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
c) In this case x is a square number, and it must be smaller than 100, so let's find all the square values smaller than 100.
1^2 = 12^2 = 43^2 = 94^2 = 165^2 = 256^2 = 367^2 = 498^2 = 649*9 = 8110*10 = 100 (from this onwards, the squares don't meet the criteria).Then this set is:
{1, 4, 9, 16, 25, 36, 49, 64, 81}
d) Here x must be an integer, such that x^2 = 2
Solving the equation we get:
x = ±√2
But √2 is an irrational number, so there is no integer number that meets this restriction, this means that we have an empty set, this is written as:
{∅}.
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Write your answer in standard form with integer coefficients.
2x + 3y = 30 ; (2,-5)
Answers
Find the product: 5(−3)(−2)
PLEASE HELP ASAP!
Answers
6(5) = 30
30 is your answer
hope this helps
Write the expression(4x-2)·6(2x 7) in the standard form of a quadratic expression, ax² bx c what are the values of the couiffeciant?
Answers
So, I will apply distributive property step by step:
1) (4x - 2) (12x - 35)
2) 4*12x^2 - 4*35x - 2*12x + 2*35 = 48x^2 - 140x - 24x + 70 = 48x^2 - 164x + 70
3) Compare with ax^2 + bx + c
=> a = 48, b = - 164, c = 70
Answer: a = 48, b = -164, c = 70
4x-3y+6z=18,-x+5y+4z=48,6x-2y+5z=0 what are x,y,and z?
Answers
4x-3y+6z=18
6x-2y+5z=0
multiply the first equation by 4 and add the results to the second equation:
-1x+5y+4z=48
17y+22z=210
6x-2y+5z=0
multiply the first equation by 6 and add the results to the third equation:
-1x+5y+4z=48
17y+22z=210
28y+29z=288
multiply the second equation by -28/17 and add the result to the third equation:
-1x+5y+4z=48
17y+22z=210
-123/17z=-984/17
solve for z
-123/17z=-984/17
z=8
then solve for y
17y+22z=210
17y+22*8=210
y=2
solve for x substituting y=2 and z=8 into the first equation:
4x-3(2)+6(8)=18
x=-6
so the solutions are x=-6, y=2, z=8
Seascapes rent small fishing boats for a day-long fishing trips. each boat can carry only 1200 lb of people and gear for safety reasons. Assume the average weight of a person is 150 lb. each group will require 200 pounds of gear for the boat plus 10 lb of gear for each person.
A) create any quality describing the restrictions on the number of people that can possibly fit in a rented boat.
B) several groups of people wish to rent a boat Group one has 4 people group two has 5 people group three has 8 people. Determine which of the groups, if any, can safely run a boat what is the maximum number of people that may rent a boat.
Answers
A. We are given that each person weighs 150 lb, each gear
per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.
Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).
So let us say that x is the number of persons, the inequality equation is:
160 x + 200 ≤ 1200
B. There are three groups that wish to rent the boat.
> Solve the inequality equation when x = 4
160 (4) + 200 ≤ 1200
840 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 5
160 (5) + 200 ≤ 1200
1000 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 8
160 (8) + 200 ≤ 1200
1480 ≤ 1200 (FALSE)
So only the 4 people group and 5 people group can safely run the boat.
C. Find the maximum number of people that may safely use the boat, solve for x:
160 x + 200 ≤ 1200
160 x ≤ 1000
x ≤ 6.25
Therefore the maximum number of people that can safely use the boat is 6 people.
A mathematical inequality is created to determine that a maximum of 6 people can rent a boat based on the safety weight limit of 1200 lb. Of the groups provided, only groups with 4 or 5 people can safely rent the boat, while the group with 8 people cannot due to exceeding the weight limit.
To determine the restrictions on the number of people that can possibly fit in a rented boat given the safety weight limit, we start by creating an inequality. Let p represent the number of people, then the total weight of the people is 150 lb times p, and the total gear weight is 200 lb for the boat plus 10 lb per person. The inequality can be represented as:
150p + 10p + 200 \<= 1200
Simplifying the inequality gives us:
160p \<= 1000
Dividing both sides by 160:
p \<= 1000 / 160
p \<= 6.25
Since we cannot have a fraction of a person, the maximum number of people allowed is 6.
For part B, we evaluate if the groups mentioned can safely rent a boat:
Group 1 (4 people): 150(4) + 10(4) + 200 = 840 lb \<= 1200 lb - they can rent.
Group 2 (5 people): 150(5) + 10(5) + 200 = 1000 lb \<= 1200 lb - they can rent.
Group 3 (8 people): 150(8) + 10(8) + 200 = 1480 lb > 1200 lb - they cannot rent as it exceeds the limit.
The maximum number of people who may rent a boat based on the given restrictions and average weights is 6 people.
Find the difference quotient and simplify your answer. f(x) = 7x − x2, f(7 + h) − f(7) h , h ≠ 0
Answers
So: f(x) = 7x - x^2, and f(7+h) - f(7)
= [7(7+h) - (7+h)^2] - [7(7) - (7)^2]
= [49+7h - 49+14h+h^2] - [49-49]
= 49-49 + 7h+14h + h^2 = h^2 + 21h =
h (h+21), h (h+21) = 0
h=0... But it stated h cannot = 0
So h+21 = 0, h = -21
The difference quotient for the function f(x) = 7x - x² is (7h - h²) / h.
Explanation:The difference quotient is used to find the rate at which a function changes over a small interval. To find the difference quotient for the given function f(x) = 7x − x², we substitute f(7 + h) and f(7) into the formula: [f(7 + h) - f(7)] / h. Simplifying the expression, we get [(7(7 + h) - (7 + h)²) - (7(7) - 7²)] / h. Expanding and simplifying further, we have [(49 + 7h - h²) - (49 - 49)] / h, which becomes (7h - h²) / h.
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#2
Point C has a _____ abscissa and a _____ ordinate.
positive, negative
negative, positive
negative, negative
positive, positive
Answers
SOMEONE PLEASE HELP!
A store allows customers to fill their own bags of candy. Troy decides he only wants chocolate-covered pretzels and gumdrops. Chocolate-covered pretzels sell for $0.89 per pound, and gumdrops sell for $0.65 per pound. Troy’s bag weighs 1.8 pounds and it cost $1.29.
A. 0.5 pounds of pretzels; 1.3 pounds of gumdrops
B. 0.9 pounds of pretzels; 0.9 pounds of gumdrops
C. 1.3 pounds of pretzels; 0.5 pounds of gumdrops
D. 0.8 pounds of pretzels; 1 pound of gumdrops
Answers
just plug in the prices of the candy .5 times the price of pretzels and 1.3 times the price of gumdrops
The regular price of a jacket is $42.75. during a sale, the jacket was marked 12% off. what was the price of the jacket during the sale? (1 point) $5.13 $30.75 $37.62 $42.63
Answers
.12x42.75=5.13
42.75-5.13=37.62
Find 3 solutions for 2x+y=10
Answers
2×3+4=10
2×2+4=10
X= 3, Y=4
(3*2+4=10)
X= 1, Y=8
(1*2+8=10)
X=4, Y=2
(4*2+2=10)
Hope this helps! :)
Divide 42 in a ratio of 1:2:3?
Answers
x+2x+3x = 42
6x = 42
6x/6 = 42/6
x = 7
Since x = 7, this means 2x = 2*7 = 14 and 3x = 3*7 = 21
Dividing 42 into the ratio of 1:2:3 means we have 7:14:21 as the answer
If we divide all three parts of 7:14:21 by the GCF 7, we reduce it down to 1:2:3
As a check,
7+14+21 = 21+21 = 42
so it works out
Write the equation of the piecewise function ƒ that is represented by its graph.
Answers
the hole, of course means, that point is not part of the range.
and the closed hole, means it is part of that range.
[tex]\bf f(x)= \begin{cases} \sqrt{x},&x\ \textless \ 4\\ x^2,&x\ge 4 \end{cases}[/tex]
Piecewise function with 3 pieces: [tex]x^2+1, 4x-8, 2[/tex]
The piecewise function ƒ that is represented by the graph in the image is:
ƒ(x) =
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
This is because the graph of the function consists of three distinct pieces:
For 0≤x<4, the graph is a parabola with vertex at (0,1) and opening upwards. This suggests that the function is of the form [tex]ax^{2} +bx+c.[/tex]
We can find the values of a, b, and c by substituting the points (0,1), (1,1), and (4,16) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]a \cdot 0^2 + b \cdot 0 + c = 1[/tex]
[tex]a \cdot 1^2 + b \cdot 1 + c = 1 \\[/tex]
[tex]a \cdot 4^2 + b \cdot 4 + c = 16[/tex]
\end{cases}
Solving this system gives us a=1, b=0, and c=1, so the equation of the function for this interval is [tex]x^{2} +1[/tex].
For 4≤x<5, the graph is a line with slope 4 and y-intercept −8.
This suggests that the function is of the form mx+b.
We can find the values of m and b by substituting the points (4,2) and (5,25) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]4m+b = 2 \\[/tex]
5m+b = 25
\end{cases}
Solving this system gives us m=4 and b=−8, so the equation of the function for this interval is 4x−8.
For x=5, the graph is a horizontal line at y=26.
This suggests that the function is of the form c.
We can find the value of c by simply looking at the graph.
This gives us c=26, so the equation of the function for this interval is 26.
Therefore, the complete piecewise function is:
ƒ(x) =
\begin{cases}
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
\end{cases}
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Simplify an expression
Answers
Answer:
[tex]\frac{20+2k}{3k+12}[/tex]
Step-by-step explanation:
Since there is no equals sign here, we are not solving this. The only way to simplify is to get a common denominator and write the expression as a single expression. We can begin by noting that the second term has a k in the numerator and in the denominator, and those cancel each other out. That is the first simplification we can perform. That leaves us with:
[tex]\frac{4}{k+4}+\frac{2}{3}[/tex]
In the first term, the denominator is k + 4, in the second term it is just 3. Therefore, the common denominator is 3(k+4). We are missing the 3 in the denominator of the first term, so we will multiply in 3/3 by that term. We are missing a (k + 4) in the second term, so we will multiply in (k + 4)/(k + 4) by that term:
[tex](\frac{3}{3})(\frac{4}{k+4})+(\frac{k+4}{k+4})(\frac{2}{3})[/tex]
Multiplying fractions requires that I multiply straight across the top and straight across the bottom. That gives me:
[tex]\frac{12}{3k+12}+\frac{2k+8}{3k+12}[/tex]
Now that the denominators are the same, I can put everything on top of that single denominator:
[tex]\frac{12+2k+8}{3k+12}[/tex]
Th final simplification requires that I combine like terms:
[tex]\frac{20+2k}{3k+12}[/tex]
A corporation employs 2000 male and 500 female engineers. a stratified random sample of 200 male and 50 female engineers gives each engineer 1 chance in 10 to be chosen. this sample design gives every individual in the population the same chance to be chosen for the sample. is it an srs? explain your answer.
Answers
No, the sample design is not a simple random sample (SRS), but a stratified random sample. In an SRS, every individual in the population has an equal chance of being chosen for the sample.
Explanation:The given sample design is not a simple random sample (SRS). In an SRS, every individual in the population has an equal chance of being chosen for the sample. However, in this case, the sample design is a stratified random sample. It involves dividing the population into groups (in this case, male and female engineers) and then selecting a sample from each group using a different sampling rate.
To determine if a sample design is an SRS, we need to ensure that each individual in the population has an equal chance of being chosen, and this probability is the same for every individual. In the case of the given example, the sample design does not meet these criteria, making it not an SRS.
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How can u tell
Whether 1080 is cube number
Answers
1080 = 2*2*2*3*3*3*5
Its not a cube because although there are 2 triplicates there is also a 5.
Note 2*2*2*3*3*3 is a cube.
The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
the number is 1080
Split into prime factors
1080 = 2*2*2*3*3*3*5
so, we have,
Its not a cube
because although there are 2 triplicates there is also a 5.
as, we know that,
Note 2*2*2*3*3*3 is a cube.
so, 1080 = 2*2*2*3*3*3*5, is not a cube number.
Hence, The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
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what is the sale tax on item that costs $33.50. if the sale tax is 0.06 on every $1?
Answers
(60 POINTS! I NEED HELP NOW PLEASE!)
Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.
-When f(x) becomes f(x) -3
-When f(x) becomes -2 * f(x)
Answers
Hugo’s friends bought used books at the yard sale Sonia paid 2.25 John paid 6.00 and Keisha paid 3.75 how many books did each friend buy
Answers
Sonia bought 9 books
John bought 24 books
Keisha bought 15 books
If each book costs 0.75, then
Sonia bought 3 books
John bought 8 books
Keisha bought 5 books
Answer:
Sonia , John and Keisha bought 3,8 and 5 books respectively.
Step-by-step explanation:
given ,
Sonia paid 2.25 to buy book in yard sale
John paid 6 to buy book in yard sale
Keisha paid 3.75 to buy book in yard sale
cost of 1 book is equal to 0.75 cent
books bought each of them will be equal to
Sonia = [tex]\dfrac{2.25}{0.75}[/tex] = 3 books
John = [tex]\dfrac{6}{0.75}[/tex] = 8 books
Keisha = [tex]\dfrac{3.75}{0.75}[/tex] = 5 books
Hence, Sonia , John and Keisha bought 3,8 and 5 books respectively.
Evaluate the expression. (26÷13)⋅(−7)+14−4 Enter your answer in the box
Answers
The value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
Simplify the expression, then the value of the expression will be
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
⇒ (2) ⋅ (−7) + 14 − 4
⇒ −14 + 14 − 4
⇒ − 4
Then the value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
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Which transformation is not isometric?
Answers
what is an equation for the number of $0.60 bagels that can be purchased with d dollars
Answers
since d is dollar and the one is
x would be the cost and the d would be the dollar
A stack of two hundred fifty cards is placed next to a ruler, and the height of stack is measured to be 5 8 58 inches.
Answers
────▐▌──────────▐▌────
────█▌▀▄──▄▄──▄▀▐█────
───▐██──▀▀──▀▀──██▌───
──▄████▄──▐▌──▄████▄──
plz don't be mad I need points
Please help!!!!!
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is ________
a. 5
b. 3
c. 2.5
d. 0.2
The slope represents _______
a. the total cost of the taxi ride
b. total number of miles traveled
c. cost per mile traveled
d. the initial cost of the taxi ride
Answers
slope = (8-3)/(2-0) = 5/2 = 2.5
answer
The slope is ________
c. 2.5
The slope represents _______
c. cost per mile traveled
The slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The function graphed shows the total cost for a taxi cab ride for x miles the cost in taxi is shown in y axis and the distance covered by taxi in x axis. Now, to find put the slope we must two coordinates which can be found out from the graph easy by observation as (0,3) and (2,8).
How using slope formula to find the slope of line :
[tex]\begin{aligned}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}&=\frac{8-3}{2-0}\\&=\frac{5}{2}\\&=2.5\end{aligned}[/tex]
It represents the cost of taxi per mile of distance travelled.
Therefore, the slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
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Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box
Answers
The solution to the inequality -32 > -5 + 9x is x > -3.
To solve the inequality -32 > -5 + 9x, we'll isolate the variable x by first getting rid of the constant term (-5) on the right side.
1. Add 5 to both sides:
-32 + 5 > 9x
-27 > 9x
2. Divide both sides by 9 to solve for x:
-27/9 > x
-3 > x
Therefore, x is greater than -3. In interval notation, this can be written as (-∞, -3). In inequality notation, it's expressed as x > -3.
We started by isolating the variable x by adding 5 to both sides, then divided by 9 to solve for x. Remember, when dividing or multiplying by a negative number, the direction of the inequality sign flips. Thus, the final solution is x > -3.
A culture started with 4,000 bacteria. After 5 hours, it grew to 4,800 bacteria. Predict how many bacteria will be present after 15 Hours.
Round your answer to the nearest whole number
Answers
The formula is
A=p e^kt
A future bacteria 4800
P current bacteria 4000
E constant
K rate of growth?
T time 5 hours
Plug in the formula
4800=4000 e^5k
Solve for k
4800/4000=e^5k
Take the log for both sides
Log (4800/4000)=5k×log (e)
5k=log (4800/4000)÷log (e)
K=(log(4,800÷4,000)÷log(e))÷5
k=0.03646
Now use the formula again to find how bacteria will be present after 15 Hours
A=p e^kt
A ?
P 4000
K 0.03646
E constant
T 15 hours
Plug in the formula
A=4,000×e^(0.03646×15)
A=6,911.55 round your answer to get 6912 bacteria will be present after 15 Hours
Hope it helps!
Answer:
6900 rounded answer -
Step-by-step explanation:
Plato users, correct.
What does negative 2 over 3 > −1 indicate about the positions of negative 2 over 3 and −1 on the number line?
Answers
Answer:
Step-by-step explanation:
Average precipitation for the first 7 months of the year, the average precipitation in toledo, ohio, is 19.32 inches. if the average precipitation is normally distributed with a standard deviation of 2.44 inches, find these probabilities.
Answers
The probability that a normally distributed data with a mean, μ and standard deviation, σ is greater than a given value, a is given by:
[tex]P(x\ \textgreater \ a)=1-P(x\ \textless \ a)=1-P\left(z\ \textless \ \frac{a-\mu}{\sigma}\right)[/tex]
Given that the average precipitation in Toledo, Ohio for the past 7 months is 19.32 inches with a standard deviation of 2.44 inches, the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is given by:
[tex]P(x\ \textgreater \ 18)=1-P(x\ \textless \ 18) \\ \\ =1-P\left(z\ \textless \ \frac{18-19.32}{2.44}\right) \\ \\ =1-P(z\ \textless \ -0.5410) \\ \\ =1-0.29426=\bold{0.7057} [/tex]
Part B:
The probability that an n randomly selected samples of a normally distributed data with a mean, μ and standard deviation, σ is greater than a given value, a is given by:
[tex]P(x\ \textgreater \ a)=1-P(x\ \textless \ a)=1-P\left(z\ \textless \ \frac{a-\mu}{\frac{\sigma}{\sqrt{n}}}\right)[/tex]
Given that the average precipitation in Toledo, Ohio for the past 7 months is 19.32 inches with a standard deviation of 2.44 inches, the probability that 5 randomly selected years will have precipitation greater than 18 inches for the first 7 months is given by:
[tex]P(x\ \textgreater \ 18)=1-P(x\ \textless \ 18) \\ \\ =1-P\left(z\ \textless \ \frac{18-19.32}{\frac{2.44}{\sqrt{5}}}\right) \\ \\ =1-P(z\ \textless \ -1.210) \\ \\ =1-0.1132=\bold{0.8868}[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.b) 0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.Normal Probability Distribution
In a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 19.32 inches, hence [tex]\mu = 19.32[/tex].The standard deviation is of 2.44 inches, hence [tex]\sigma = 2.44[/tex].Item a:
The probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is 1 subtracted by the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 19.32}{2.44}[/tex]
[tex]Z = -0.54[/tex]
[tex]Z = -0.54[/tex] has a p-value of 0.2946.
1 - 0.2946 = 0.7054.
0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.
Item b:
Now, we want the probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months, hence:
[tex]n = 5, s = \frac{2.44}{\sqrt{5}}[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 19.32}{\frac{2.44}{\sqrt{5}}}[/tex]
[tex]Z = -1.21[/tex]
[tex]Z = -1.21[/tex] has a p-value of 0.1131.
1 - 0.1131 = 0.8869.
0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
List -0.3 , 0.5 ,0.55 ,-0.35 from least to greatest
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