Answer:
0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles
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 establishes 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 number of miles between services is 4959 miles, with a standard deviation of 448 miles
This means that [tex]\mu = 4959, \sigma = 448[/tex]
Sample of 43:
This means that [tex]n = 43, s = \frac{448}{\sqrt{43}}[/tex]
What is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles?
p-value of Z when X = 4959 + 111 = 5070 subtracted by the p-value of Z when X = 4959 - 111 = 4848, that is, probability the sample mean is between these two values.
X = 5070
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5070 - 4959}{\frac{448}{\sqrt{43}}}[/tex]
[tex]Z = 1.62[/tex]
[tex]Z = 1.62[/tex] has a p-value of 0.9474
X = 4848
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4848 - 4959}{\frac{448}{\sqrt{43}}}[/tex]
[tex]Z = -1.62[/tex]
[tex]Z = -1.62[/tex] has a p-value of 0.0526
0.9474 - 0.0526 = 0.8948
0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles
what are all the factos of 36
Hi there!
»»————- ★ ————-««
I believe your answer is:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
»»————- ★ ————-««
Here’s why:
A factor is a whole number that is multiplied by another to have a product have another number.
⸻⸻⸻⸻
The Factors Are:
1 (1 * 36 = 36)2 (2 * 18 = 36)3 (3 * 12 = 36)4 (4 * 9 = 36)6 (6 * 6 = 36) 9 (9 * 4 = 36)12 (12 * 3 = 36)18 (18 * 2 = 36)36 (36 * 1 = 36)⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Which statement best describes g(x) = 3x + 6 - 8 and the parent function f(x) = } ?
The domains of g(x) and f(x) are the same, but their ranges are not the same.
* The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
In general gf(x) is not equal to fg(x)
Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.
Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.
Step-by-step explanation:
g(x) = 3x + 6 - 8, f(x) = √x.
The domain of a composed function is either the same as the domain of the first function, or else lies inside it
The range of a composed function is either the same as the range of the second function, or else lies inside it.
Or vice versa
Now only positive numbers, or zero, have real square roots. So g is defined only for numbers
greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or
equal to zero. You can work out that
f(x) ≥ 0 only when x ≥3/2
.
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
2.7.2 : Checkup - Practice Problems
A professor creates a histogram of test scores for 26 students in a statistics course. What is the probability of a student having scored between 65 and 100
Complete Question
Complete is Attached Below
Answer:
Option D
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=26[/tex]
Student scoring [tex]65-100 n'=12[/tex]
Generally the equation for probability of a student having score between 65 and 100 is mathematically given by
[tex]P(65-100)=\frac{12}{26}[/tex]
[tex]P(65-100)=12/26[/tex]
[tex]P(65-100)=0.462[/tex]
Option D
The sum of two numbers is 44 . One number is 3 times as large as the other. What are the numbers?
Answer:
11 and 33
Step-by-step explanation:
The the smaller number be [tex]x[/tex]. Since the other number is 3 times as large as the other, we can represent the large number as [tex]3x[/tex]. Because they add up to 44, we have the following equation:
[tex]x+3x=44[/tex]
Combine like terms:
[tex]4x=44[/tex]
Divide both sides by 4:
[tex]x=\frac{44}{4}=\boxed{11}[/tex]
Substitute [tex]x=11[/tex] into [tex]3x[/tex] to find the larger number:
[tex]11\cdot 3=\boxed{33}[/tex]
Therefore, the two numbers are 11 and 33.
PLEASE HELP WILL MARK BRAINLIEST
Answer:
AB
Step-by-step explanation:
From the question given above, we were told that triangle ABC is similar to triangle PTG.
Since both triangles are similar, the following assumptions hold:
PG / AC = PT / AB = TG / BC
Comparing the equation above with those given in the question, the missing part of the equation is AB
What is the solution to the linear equation?
-12 + 3b - 1 = -5 - b
Answer:
b=2
Step-by-step explanation:
We roll a pair dice 10,000 times. Estimate the probability that the number of times we get snake eyes (two ones) is between 280 and 300.
Answer:
0.3573 = 35.7%
Step-by-step explanation:
We roll a pair of dice 10,000 times so the mean and standard deviation is,
μ = 10000/36 =277.7 σ = [tex]\sqrt{10000*\frac{35}{36^{2} } } =16.4[/tex]
[tex]z_{1}[/tex] = (280 - 277.7)/16.4 = .14
[tex]z_{2}[/tex] = (300 - 277.7)/16.4 = 1.35
Probablity (range)
0.3573
Z(low)=0.14 0.555766357
Z(upper)=1.36 0.91304644
At a bake sale, pies cost $8 each. One customer buys $64 worth of pies.
The customer bought 8 pies.
To find the total amount of pies the customer bought, simply divide 64 by 8 to recieve your answer of 8 pies.
I hope this is correct and helps!
2•^4= ?
A) 1/16
B) 1/8
C) 1
Answer:
1/16.
Step-by-step explanation:
2^-4 = 1/2^4
= 1/16.
haydenkyletoddhaydenkyletodd
Multiple choice plss help
Answer:
D
Step-by-step explanation:
The correct answer Is D
Question
The sum of three consecutive even integers is -312. Find the Integers.
Answer:
-105, -104, -103
Step-by-step explanation:
lets the numbers be:
x
x+1
x+2
so:
x+(x+1)+(x+2)=-312
x+x+x+1+2=-312
3x+3=-312
3x=-312-3=-315
x=-315/3=-105
in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.
Answer:
ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem
ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem
Step-by-step explanation:
First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.
Second set :
[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{EF}{RF}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{FG}{FQ}[/tex] = [tex]\frac{20}{24}[/tex] = [tex]\frac{5}{6}[/tex]
Need help ASAP
HELP PLEASEE
Can someone help me?
Answer:
x = 80
Step-by-step explanation:
3x/2=120°
3x=240°
x=80°
Answered by GAUTHMATH
In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect
Answer:
15ways
Step-by-step explanation:
This is a combination question since combination has to do with selection. Hence the number of ways sample of 6 keyboards can be selected so that exactly two have an electrical defect is expressed as;
6C2 = 6!/(6-2)!2!
6C2 = 6!/4!2!
6C2 = 6×5×4!/4!×2
6C2 = 6×5/2
6C2 = 30/2
6C2 = 15
Hence this can be done in 15ways
whether the distribution of the mean of a large number of independent, identically distributed variables. true or false
Answer:
The statement is false
Step-by-step explanation:
Given
See comment for complete statement
Required
Is the statement true or false
From central limit theorem, we understand that a distribution is approximately normal if the distribution takes a sample considered to be large enough from the population.
Also, the mean and the standard deviation are known.
However, the given statement implies that the distribution will be normal depending on an underlying distribution; this is false.
(6a/8+3) + 7a/8...........
Hello!
(6a/8+3) + 7a/8 =
= 6a/11 + 7a/8 =
= 125/88 × a
Good luck! :)
How do I make people brainliest
Answer:
you have to wait until two people answer then you click their answer to make them brainliest
Step-by-step explanation:
i dont know
blah blah blah blah blah blah blah blah blah blah blah blah
6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)
Answer:
21/8x
Step-by-step explanation:
10x -20 = -6x+22
+6x-20 = 22
16x-20 = 22
16x +20= +20
16x/16x = 42/16x
x = 21/8x
Find the appropriate answer for each word problem.
a. A group of twelve art students are visiting a local art museum for a field trip. The total cost of admission for the students is $125. What is the cost of admission for each student?
b. The school van can carry twelve passengers at a time. What is the least number of trips the van must make in order to bring 125 passengers to the same location?
c. Charlotte and her mother baked 125 cookies to give as Christmas gifts to their neighbors. If they plan to give a dozen cookies to each neighbor, how many neighbors will receive a gift?
d. Nicholas and Elaine are planning to serve cheesecake for dessert at their wedding and have purchased twelve cheesecakes. If the cheesecakes are divided evenly among the 125 wedding guests, how much cheesecake will each guest receive?
I WILL GIVE BRAINLIEST IF CORRECT
Answer:
a. $10
b. 10.46
c. 10.46
d. 0.096
What is the missing term in the factorization?
12x2 – 75 = 3 (2x+?)(2x – 5)
Answer:
12x2 – 75 = 3 (2x+5)(2x – 5)
Step-by-step explanation:
The cost of renting a car is $46/week plus $0.25/mile traveled during that week. An equation to represent the cost would be y = 46 + 0.25x, where x is the number of miles traveled.
what is your cost if you travel 59 miles
cost: 60.75
if your cost Is $66.00, how many miles were you charged for traveling?
miles: ?
you have a max of $100 to spend on a car rental. what would be the maximum number of miles you could Travel?
max miles: ?
Answer:
If your cost Is $66.00, how many miles were you charged for traveling?
y = cost = $66[tex]66=46+0.25x\\66-46=0.25x\\20=0.25x\\x=\frac{20}{0.25} =80[/tex]80 miles
You have a max of $100 to spend on a car rental. what would be the maximum number of miles you could Travel?
y = cost = $100[tex]100=46+0.25x\\100-46=0.25x\\54=0.25x\\x=\frac{54}{0.25} =216[/tex]216 miles
A researcher conducts a repeated-measures design study comparing 2 treatment conditions and obtains 20 scores in EACH treatment condition. How many participants participated in the study
Answer:
20 participants
Step-by-step explanation:
Given
[tex]Conditions = 2[/tex]
[tex]Scores = 20[/tex]
Type: Repeated design
Required
The number of participants (n)
The repeated measure design implies that the test was conducted repeatedly on the same sample size.
Since the score in each test is 20; then:
[tex]n = 20[/tex] --- the number of participants
Find the volume (in cubic inches) of an exercise ball with a radius of 14 inches. (Round your answer to one decimal place.)
Answer:
11,494.0³
Step-by-step explanation:
Volume of a sphere= (4/3) × pi × radius³
4÷3 × 3.14 ×14³
= 11,494.0³
10. Football: A kicker on a professional football
team made 45 of 48 field goal attempts.
a. What percent of his attempts did he
make?
b. What percent did he miss? Would you keep
this player on your team or trade for a new
kicker?
Answer:
a) 93.75%; 6.25%
b) Keep :)
Step-by-step explanation:
1. Made percentage[tex]\frac{45}{48}=0.9375=93.75[/tex]
93.75% made
2. Missed percentage[tex]\frac{3}{48}=0.0625=6.25[/tex]6.25% missed
Hope this helped! Please mark brainliest :)
The average of 6,10,x,20 and 30 is 18. what is the value of x
Answer:
24
Step-by-step explanation:
18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)
so,
6+10+20+30=66
90-66=24
I hope this helps!
Answer:
[tex]x = 24[/tex]
Step-by-step explanation:
[tex]6 + 10 + x + 20 + 30 = 18[/tex]
There are 5 numbers that we must add to average out to get 18 so let set this equation up
[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]
[tex]6 + 10 + x + 20 + 30 = 90[/tex]
[tex]x = 24[/tex]
1) What is the opposite of adding 5?
2) What is the opposite of subtracting 20?
3) What is the opposite of multiplying by 1/2?
4) What is the opposite of dividing by 10?
Answer:
1) subtracting 5
2) adding 20
3) dividing by 2 (multiplying by 1/2)
4) multiplying by 1/10 (dividing by 10)
Step-by-step explanation:
There are four main operations in math: adding, subtracting, multiplying, and dividing. Each of the operations has an opposite. Adding and subtracting are opposites and multiplying and dividing are opposites. This means that subtracting can undo adding and vice versa; additionally, dividing can undo multiplying or vice versa. So, to find the opposite of something switch the operation to the opposite and keep the number. However, it is important to note that with multiplying and dividing you can also find the opposite by keeping the operation while changing the number to the reciprocal.