Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Answer:
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
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.
If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.
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.
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Sample of 3
This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]
Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
We have to find the z-score.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]
[tex]Z = 1.73[/tex]
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
Suppose a researcher found an rs of .89 between amount of blood cholesterol and the severity of the heart attack. Based on an N of 6 and a two-tailed test, the researcher should conclude:_________.a. not significantb. significant at the .05 levelc. p > .05d. higher blood cholesterol causes more severe heart attacks
Answer:
d. higher blood cholesterol causes more severe heart attacks.
Step-by-step explanation:
Two tailed tests are a method for hypothesis testing when data is distributed on the two sides. P value is determined to identify whether the hypothesis is true or false. When rs is 0.89 between blood cholesterols and severity of heart attacks then these is significant relation between them.
if you help me with this i will mark you brainly-est but you gotta tell me how to because i don't know how ? \
Answer:
1/6
Step-by-step explanation:
Rhianna has 3/6 or 1/2 of a box of pencils
When she divides 3/6 among three people, you get 1/6
Each friend gets 1/6 of a box
In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. Suppose you are a news reporter following twelve criminal trials.
(a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? What is this probability if the trials were in the United States?
(b) Of the ten trials, what is the expected number of guilty verdicts in Japan? What is the expected number in the United Sates? What is the standard deviation in each case?
Answer:
a) Japan =0.599
US= 0.006
b) Japan
Variance= 0.475
Standard Deviation =0.69
USA
Variance =2.4
Standard Deviation= 1.55
Step-by-step explanation:
A represents the number of defendants found guilty in Japan in 10 trials
B represents the number of defendants found guilty in US in 10 trials
A represents a binomial function such that n=10,p=0.95 and B represents a binomial function such that n=10,p=0.60
a) Japan: P(A=10)=0.95^10=0.599
US: P(B=10)=0.60^10=0.006
b) Japan:
Expected number of guilty verdicts in 10 trials in Japan = np=10*0.95=9.5
Variance: Var(A) = np(1-p) = 10*0.95*(1-0.95) = 0.475
Standard Deviation = sd(A)=√0.475=0.69
US:
Expected number of guilty verdicts in 10 trials in USA = np=10*0.60=6
Variance: Var(B)=np(1-p)=10*0.6*0.4=2.4
Standard Deviation sd(B)=√2.4=1.55
A rectangular room is 1.2 1.2 times as long as it is wide, and its perimeter is 35 35 meters. Find the dimension of the room.
Answer:
I. Length, L = 9.552 meters
II. Width, W = 7.96 meters
Step-by-step explanation:
Let the length = L
Let the width = W
Given the following data;
Perimeter = 35 m
Translating the word problem into an algebraic equation, we have;
Length = 1.2W
To find the dimension of the room;
The perimeter of a rectangle is given by the formula;
P = 2(L + W)
Substituting into the formula, we have;
35 = 2(1.2W + W)
35 = 2(2.2W)
35 = 4.4W
Width, W = 7.96 meters
Next, we would find the length of the rectangle;
L = 1.2*W
L = 1.2 * 7.96
Length, L = 9.552 meters
Which values are NOT in the domain of the function?
f(x)
x +4
x2 – 25
O
A) x = -4,4
B) 2 = -5,4
C) x = -4,5
OD) X = -5,5
Given:
The function is:
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
To find:
The values that are NOT in the domain of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
This function is a rational function and it is defined for all real values of x except the values for which the denominator is equal to 0.
Equate the denominator and 0.
[tex]x^2-25=0[/tex]
[tex]x^2=25[/tex]
Taking square root on both sides, we get
[tex]x=\pm \sqrt{25}[/tex]
[tex]x=\pm 5[/tex]
So, the values [tex]x=-5,5[/tex] are not in the domain of the given function.
Therefore, the correct option is D.
Sadie brought $28.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/3 as much as the sketchbook, and the sketchbook cost 1/2 the cost of the paint set. Sadie had $3.00 leftover after buying these items. What was the cost of each item?
Answer:
cost of paint set = $ 13.64
cost of sketch book = $ 6.82
cost of brush = $ 4.55
Step-by-step explanation:
Let the cost of paint set is s.
cost of sketch book = s/2
cost of brush = s/3
Money spent = $ 28 - $ 3 = $ 25
So,
s + s/2 + s/3 = 25
6 s + 3 s + 2 s = 150
11 s = 150
s = $ 13.64
cost of paint set = $ 13.64
cost of sketch book = $ 6.82
cost of brush = $ 4.55
Tom worked the following hours last week but he needs to complete his timesheet in decimals
Answer:
Monday: 7.25
Tuesday: 6.75
Wednesday: 5.2
Thursday: 6.1
calculus help needed!
Answer:
No
Not continous at x = 6
Step-by-step explanation:
When x = 6
G(6) = 1/(6 - 6) = 1/0
Dividing by 0 creates a discontinuity
Rewrite |3x+5|<or equals to 1 without absolute
value sign
Answer:
remember how the absolute value works:
|x| = x if x ≥ 0
|x| = -x if x < 0
Then we can rewrite:
|x| ≤ a
as:
-a ≤ x ≤ a
Now let's apply this to our case:
|3x + 5| ≤ 1
we can rewrite this as:
-1 ≤ 3x + 5 ≤ 1
We could solve this for x now, first subtracting 5 in the 3 sides:
-1 - 5 ≤ 3x + 5 - 5 ≤ 1 - 5
-6 ≤ 3x ≤ -4
now dividing by 3 in the 3 sides:
-6/3 ≤ 3x/3 ≤ -4/3
-2 ≤ x ≤ -(4/3)
So we rewrote the inequality without the absolute value part.
The shortest route from London to Oxford is 55 miles.
A lorry is expected to take 1.1 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 1.1 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
so to find the mph of the lorry for the original route we divide 66 by 55 since it 66 is 1.1 of 60
66 divided by 55=1.2
so it takes 1 minutes 12 seconds for the lorry to go a mile
now we multiply 55 by 1.15=63.25
so we divide 66 by 63.25=1.04347826087
so it takes 1 minute and 1 second for the the lorry to go a miles
1 minute 1 second is 59 miles per hour
1 minute 12 seconds is 50 miles per hour
so the lorry travels 9 mph over its expected speed
Hope This Helps!!!
=================================================
Explanation:
distance = rate*time
d = r*t
r = d/t
r = 55/1.1
r = 50
The lorry's original speed is 50 mph when going the original route.
-----------------
Now consider the longer route, which is 15% longer compared to the original 55 mile route. So the longer route is 1.15*55 = 63.25 miles exactly. Or you could say 15% of 55 = 0.15*55 = 8.25 which adds onto the original 55 to get 55+8.25 = 53.25; either way the longer distance is 63.25 miles.
Computing the new rate or speed gets us
r = d/t
r = 63.25/1.1
r = 57.5
-----------------
When traveling the original route, the lorry goes 50 mph. When traveling the longer route, the lorry goes 57.5 mph. This is a difference of 57.5 - 50 = 7.5 mph
Meaning that the lorry must drive 7.5 mph faster on the longer route compared to the shortest route. This is if the driver wants to make the trip in the same 1.1 hour timeframe.
Note: 1.1 hours = 1.1*60 = 66 minutes = 1 hour, 6 minutes.
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answer:
C. -2x +3y-6=0
this is the answer
The vertices of ABC are A (5,5), B (-3,-1) and C (1,-3). Explain how would you verify that ABC is a right triangle.
Answer:
For that you should prove Ac²=Ab²+Bc²
Step-by-step explanation:
Use distance formula for finding each distance Ac,Ab and BC and prove "Ac²=Ab²+Bc²" as true
Weekly demand for a certain brand of a golf ball at The Golf Outlet is normally distributed with a mean of 35 and a standard deviation of 5. The profit per box is $5.00. Write an Excel formula that simulates the weekly profit:
= 5 * 35 * NORMSINV(RAND())
= 5* NORMINV(RAND(), 35, 5)
= 5 * RANDBETWEEN(5, 35)
= NORMINV(RAND(), 5 * 35, 5)
Answer:
= 5 * NORMINV(RAND(), 35, 5)
Step-by-step explanation:
From the given information:
The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.
Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.
Using the Excel Formula:
The weekly profit can be computed as:
= 5 * NORMINV(RAND(), 35, 5)
How many different license plates are possible if digits and letter can be repeated if the configuration is 3 letters, 2 digits, 2 letters?
Answer:
1,188,137,600 possible combinations
Step-by-step explanation:
The first three and last two digits can be any letter while the middle two digits can be any number.
26*26*26*10*10*26*26=1,188,137,600
Find the cost of eight apples at 50c each, three oranges at 35c each and 5 kg of bananas at
$2.69 per kilogram. show your working.
Answer:
1850 cents or $18.50
Step-by-step explanation:
50*8=400
3*35=105
5*269=1345 ($2.69 can be converted to 269 cents)
400+105+1345=1850
Sarah bought a TV for £250
Three years later she sold it for £180
Work out her percentage loss
Answer:
36%
Step-by-step explanation:
Step-by-step explanation:
Loss percentage= loss/cost× 100%
250-180=70
70/180=0.3888
0.3888×100%=39%
The student council has 30 male members and 25 female members. What is the ratio of male student council members to female?
rosa can run 400 meters in one min. if she runs at the same rate how may meters can she run in 5 min
Answer:
2000 meters
Step-by-step explanation:
400 * 5
David has available 240 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
Below in bold.
Step-by-step explanation:
Perimeter = 2*width + 2*length
So
240 = 2w + 2l
120 = w + l
l = 120 - w
(a) Area = w*l
Substituting for l:
A = w(120 - w)
A = 120w - w^2
(b)
Finding the derivative:
A = 120w - w^2
A' = 120 - 2w
For a maximum area A' = 0, so:
120 - 2w = 0
2w = 120
w = 60 yards for maximum area.
(c)
Maximum area
= 120*60 - 60^2
= 3600 yd^2.
Carly withdraws $18 from her bank account. Which number line represents this amount?
Write down the equation of the function whose graph is shown.
will mark brainliest
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
drink sales for an afternoon at the school carnival were recorded in the table. What is the experimental probability that the next drink is a small cocoa
Answer:
Not enough data
Step-by-step explanation:
simplify the following 4√28÷3√7
[tex]\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }[/tex]
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V r2h
-
Write the formula to calculate the height, h.
Step-by-step explanation:
V should be written as (1/3) pi r^2 h
V = (1/3) pi r^2 h multiply by 3
3V = pi r^2 h Divide by pi
3V/ pi = r^2 h Divide by r^2
3V / (pi *r^2 ) = h
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
ANSWER ALL QUESTIONS
1. In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How
many pupils have both pencils and erasers?
2. A universal set, U consists of prime numbers with P and Q as subsets of U. If P and Q are given by
P = {n: 3(n + 1) = 2(n + 10)}, and Q = {n: 7<n<31}, list the elements of P n Q.
1. 3
29-9=19
13+9=22
22-19=3
I don't know number 2, sorry.
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
An inverse function is y = k/x
replace x and y with the given values:
6 = k/18
Solve for k by multiplying both sides by 18:
k = 108
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
Solution:-[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]
Substitute the values to find k:
[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]
[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]
[tex]\sf\rightarrow{k=(6)(18)}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]
Answer:-[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]
[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]
#CarryOnMath⸙
Robert and Chris can skate 4 miles in 18 minutes. How far can they ride in 45 minutes?
Answer: Robert and Chris can skate 10 miles in 45 minutes.
Step-by-step explanation:
Let's start by finding the unit rate.
[tex]\frac{4}{18} =\frac{2}{9} \\\frac{18}{18} =1[/tex]
Robert and Chris can skate [tex]\frac{2}{9}[/tex] of a mile in 1 minute. Now we can multiply both by 45 to see how far the can go in 45 minutes.
[tex](\frac{2}{9}) (\frac{45}{1} )\\\frac{(2)(45)}{(9)(1)} \\\frac{90}{9} \\10[/tex]
45x1=45
The can skate 10 miles in 45 minutes.