Answer:
0.2061 = 20.61% probability that the mean of the women will be more than 1.5 points higher than the mean of the men
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Women:
Mean 5, standard deviation 1.5.
Sample of 12.
So
[tex]\mu_{W} = 5[/tex]
[tex]s_{W} = \frac{1.5}{\sqrt{12}} = 0.433[/tex]
Men:
Mean of 4, standard deviation 1.5.
Sample of 12.
So
[tex]\mu_{M} = 4[/tex]
[tex]s_{M} = \frac{1.5}{\sqrt{12}} = 0.433[/tex]
What is the probability that the mean of the women will be more than 1.5 points higher than the mean of the men?
This is:
[tex]P(W - M) \geq 1.5[/tex]
Subtraction:
[tex]\mu_{W-M} = \mu_{W} - \mu_{M} = 5 - 4 = 1[/tex]
[tex]s_{W - M} = \sqrt{s_{W}^2+S_{M}^2} = \sqrt{0.433^2+0.433^2} = 0.6124[/tex]
The probability is 1 subtracted by the pvalue of Z when X = 1.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this distribution
[tex]Z = \frac{X - \mu_{W-M}}{s_{W - M}}[/tex]
[tex]Z = \frac{1.5 - 1}{0.6124}[/tex]
[tex]Z = 0.82[/tex]
[tex]Z = 0.82[/tex] has a pvalue of 0.7939
1 - 0.7939 = 0.2061
0.2061 = 20.61% probability that the mean of the women will be more than 1.5 points higher than the mean of the men
WILL MARK BRAINLEIST HELPP PLEASEEEE
Answer:
15
Step-by-step explanation:
9x + 25 + x + 5 = 180
Add numbers = (25 + 5 = 30)
9x + 30 + x = 180
Combine like terms = (9x + x = 10x)
10x + 30 = 180
Subtract 30 from each side (10x + 30 - 30 = 180 - 30)
10x = 150
Divide 10 from each side (10x/10 = 150/10)
x = 15
can somebody help me?
does ''-3.5 · 12" equal ''-42 "?
Answer:
i think they equal
Step-by-step explanation:
What is the slope-intercept equation for the line below?
5
(4,3)
(0, 1)
5
O A. y=2x+1
B. y=-3x+1
O C. y=-2x+1
O D. y = 2x+1
Answer:
is there a pic you could provide?
Step-by-step explanation:
The slope-intercept equation for the line is,
⇒ y = 1/2x + 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (4, 3) and (0, 1).
Now,
Since, The equation of line passes through the points (4, 3) and (0, 1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 3) / (0 - 4)
m = - 2 / - 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 3 = 1/2 (x - 4)
⇒ y - 3 = 1/2x -2
⇒ y = 1/2x + 1
Therefore, The slope-intercept equation for the line is,
⇒ y = 1/2x + 1
Learn more about the equation of line visit:
https://brainly.com/question/18831322
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In ΔCDE, the measure of ∠E=90°, the measure of ∠C=78°, and DE = 2.2 feet. Find the length of EC to the nearest tenth of a foot.
Answer:
0.5
Step-by-step explanation:
deltamath
Answer:
the correct answer is 0,5
Step-by-step explanation:
im confused ab this i didnt learn this
Answer:
90Step-by-step explanation:
30% of 90 = 27
To explain this in a simple way we can check the work
10% of 90 = 9
9 x 3 = 27
I really need help with this statistical/variable question, i am really struggling and would be super happy if someone could answer
Answer:
Statistic
Step-by-step explanation:
A statistic is a sample of the whole mean like
E.x( how many pink doughnuts are in the dozen pack of doughnuts.
A parameter represent the whole mean
E.x( how many donuts were made at 7:00)
Since they are sampling 25 cars, it is a statistic.
Which of the following are true statements? Select two that apply.
Answer:
Options A and C are correct answers
Step-by-step explanation:
A) [tex] \angle 5\: and \:\angle 1[/tex] are complementary.
C) [tex] \angle 3\: and \:\angle 4[/tex] form a linear pair.
Hope it helps you in your learning process.
WILL MARK BRAINLELIST HELPPPP ME
Answer:
17
Step-by-step explanation:
180 - 5 - 5 = 170 : 2 = 85 : 5 = 17
e^x is greater than or equal to 25
In a bag of blue and yellow candies, the ratio of blue candies to yellow candies is 3:5. If the bag contains 60 yellow candies, how many blue candies are there?
Answer:
36 blues
Step-by-step explanation:
Answer:
36 blue Candies
Step-by-step explanation:
Let
x ----> the number of blue Candies
y ----> the number of yellow Candies
we know that
The ratio of blue candied and yellow candies is 3:5
Step-by-step explanation:
The ratio of blue candied and yellow candies is 3:5
so
x = 3
y 5 -----> equation A
the bag contains 60 yellow Candies
so
y=60 ----> equation B
substitute equation B in equation A
r 3
60 5
solve for x
x=3 (60) = 36
5
What is the midpoint of the segment (2,4) (2,-7)
Answer:
b
Step-by-step explanation:
Can someone help meee
Answer:
A= 90 (right angel )
E= 90 - 67 = 23
I hope im right!!
The students in Jamie's grade voted to select a guest speaker. 75% of
the students voted for a famous athlete. If there are 48 students in Jamie's
grade, how many students voted for the athlete?
can somebody help me?
Answer:
1.− 12 b + 6 c + 18
2.− 6 ( 2 b − c − 3 )
Step-by-step explanation:
hope that helps
if correct please mark as brainliest
thank you
:)
It takes Phillip 11 hours to proof read a chapter of hawked learning systems college algebra book and it takes Cynthia 4 hours. how long would it take them working together?
Help please I give brainliest
Answer:
(8,5)
Step-by-step explanation:
Your X coordinate would determine how far right or left something would be on a plot. The more left, the lower the number, and the more right, the higher the number. Y coordinate controls the height. Therefore, the coordinates with the highest X value would be the answer.
The radius of a cylindrical construction pipe is 1.5ft. If the pipe is 17ft long
Answer:
The volume is 120.11ft^3
Step-by-step explanation:
Given
[tex]r = 1.5ft[/tex]
[tex]l = 17ft[/tex]
Required
Determine the volume
This is calculated as:
[tex]V = \pi r^2h[/tex]
h, in this case represents the length;
So, we have:
[tex]V = 3.14 * 1.5^2 * 17[/tex]
[tex]V = 120.11ft^3[/tex]
Can someone please help meeee I’m desperateeee
Answer:
Step-by-step explanation:
1)(-3x+10)(50-x)=180
-4x+60=180
-4x=120
x=-30
2)6x+2+2x=90
8x=88
x=11
larger angle: 68°
3) a=3x°
4)(7x-5)=-2x+22
9x=27
x=3
DBE=16°
5)(x-39)=2x-59)
x=20
ILL GIVE BRAINLESTTTTT
Answer:
11/6 - 5/6 = 6/6
Step-by-step explanation:
PLEASE HELP ME ANSWER THIS QUESTION!!! Last question!!
Answer:
you got this
Step-by-step explanation:
trust your instincts so that way you may succeed in your collage
Answer
Angle 1=112 degrees
Step-by-step explanation:
Aight so we know angle 1 nd 2 equals 180 degrees, and because of some theorem with lines, angles 2 and 4 are both alternate exterior angles which means they are the same.
So if angle 4=5x+13
and angle 1=10x+2
and together they make 180, this should be your equation:
5x+15=180
simplify to get x=11
then since 1 =10x+2
multiply 11 by 10 then add 2
and your final answer should be 112 degrees
hope this helps
Bill invests $3000 in a bound fund with an interest rate of 9% per year. If bill does not withdraw any money, in how many years will his bond fund be worth $5000?
Answer:
around 5.93 years
Step-by-step explanation:
A=P(1 + r/n)^n(t)
5000=3000(1 + .09/1)^1(t)
If the perimeter of the rectangle is 52 inches, find the value of x -
height is (x+2) inches
length is 3x-1 inches
Answer:
25/4
Step-by-step explanation:
perimeter is total length of all side
height =2(x+2) (×2 bcause has 2 side)
length =2(3x-1) (×2 bcause has 2 side)
2x+4+6x-2=52
8x-2=52
8x=50 (8x is 8 times x, so move to the other side become divide)
x=50/8
simplify
x= 25/4
Leslie wants to build a 1,200 piece jigsaw puzzle. The completed puzzle will be in the shape of a rectangle that is 40 pieces in length by 30 pieces in width. Each piece is a square with an area of 0.25 in2. If Leslie wants to build the puzzle on a table that is at least 6 inches larger on all four sides than the complete puzzle, so that it makes a 6-inch border around the puzzle, what are the minimum dimensions of the table that she will need?
Answer:
If the area of each square piece is 0.25 in, that means that the dimensions must be 0.5 in by 0.5 in. Because the puzzle is 40 pieces by 30 pieces, that gives dimensions of 20 in by 15 in. Adding 6 inches on all four sides of the puzzle, we will have 32 in by 27 in for our minimum table dimensions.
Step-by-step explanation:
If the area of each square piece is 0.25 in, that means that the dimensions must be 0.5 in by 0.5 in. Because the puzzle is 40 pieces by 30 pieces, that gives dimensions of 20 in by 15 in. Adding 6 inches on all four sides of the puzzle, we will have 32 in by 27 in for our minimum table dimensions.
(1 p 18. Demarcus drew a pair of complementary angles. He drew one angle that had a measure of 48º. What was the measure of the other angle he drew? 42° 48° O 132° O 138°
Answer: 42
Step-by-step explanation:
Complementary angles are angles in which the sums equal 90.
90 - 48 = 42.
In the year 2001, a company made $5.5 million in profit. For each consecutive
year after that, their profit increased by 12%. How much would the company's
profit be in the year 2003, to the nearest tenth of a million dollars?
The approximate length (in cm) of a typical Pacific halibut t years old is given by f(t) = 200(1 -0.956e-0.181).
A Pacific lialibut caught by Mike measures 140cm. What is its approximate age?
Answer:
6 years old
Step-by-step explanation:
Given
[tex]f(t) = 200(1 -0.956e^{-0.18t})[/tex]
Required
Find t when f(t) = 140cm
Substitute f(t) = 140cm
[tex]140 = 200(1 -0.956e^{-0.18t})[/tex]
Divide both sides by 200
[tex]0.7 = 1 -0.956e^{-0.18t}[/tex]
Collect like terms
[tex]0.956e^{-0.18t} = 1 -0.7[/tex]
[tex]0.956e^{-0.18t} = 0.3[/tex]
Solve for t
[tex]e^{-0.18t} = 0.3/0.956[/tex]
[tex]e^{-0.18t} = 0.31381[/tex]
Take natural logarithm of both sides
[tex]ln(e^{-0.18t}) = ln(0.31381)[/tex]
[tex]-0.18tln(e) = ln(0.31381)[/tex]
[tex]-0.18t*1 = ln(0.31381)[/tex]
[tex]-0.18t = -1.159[/tex]
Solve for t
[tex]t = (-1.159)/(-0.18)[/tex]
[tex]t = 6.43[/tex]
[tex]t \approx 6[/tex]
Substitution method. Help!
Answer:
(2, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 3x - 4
2y = -x + 6
Step 2: Solve for x
Substitution
Substitute in y: 2(3x - 4) = -x + 6[Distributive Property] Distribute 2: 6x - 8 = -x + 6[Addition Property of Equality] Add x on both sides: 7x - 8 = 6[Addition Property of Equality] Add 8 on both sides: 7x = 14[Division Property of Equality] Divide 7 on both sides: x = 2Step 3: Solve for y
Substitute in x [Original Equation]: y = 3(2) - 4Multiply: y = 6 - 4Subtract: y = 2z=-5x(x-20) solve for x
Step-by-step explanation:
there is no solution
Miles : 3/5
Hours : 1/3
_____ miles in 1 hour
Answer:
9/5 miles in 1 hour
Step-by-step explanation:
As we are finding here the miles distance in 1 hour so we have to use here the formula which is
Rate = Distance / Time
Rate = 3/5 divided by 1/3
SO using third proportion rule we have to change the Numerator of second fraction with denominator and denominator with numerator and division sign will be change into Multiplication so this one will be
3/5 x 3/1
9/5 will be the answer