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
The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.
Answer: [tex]73^{\circ}[/tex]
Step-by-step explanation:
Angles in a triangle add to 180 degrees.
Determine the slope of the line whose equation is 2x-3y=5
3/2 inches snow fell in 3/4 of an hour which two statements are true
Answer:
I don't see the two statements
Step-by-step explanation:
Answer:
A and E Usa test prep
Step-by-step explanation:
I know it might be late by now but this is for the people who are searching for the answer for the future
How many cups are in 16 gallons?
64
256
128
2,048
Answer:
256 cups
Each gallon has 16 cups so 16 gallons would have 16*16 cups. 16*16 = 256
Ford provides an option of a sunroof and side air bag package for its Windstar model. This package costs$1400. Ford wants todetermine the percentage of Windstar buyers who would pay $1400 extra for the sunroof and side air bags. How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers
Answer:
601 buyers must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers?
We need to survey n buyers. n is found when [tex]M = 0.04[/tex]. We dont have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]
[tex]n = 600.3[/tex]
Rounding up
601 buyers must be surveyed.
mario is saving his money in order to buy a new video game, he decides to save $5 of his allowance every week. the equation he writes to describe the total amount of money he will save each week is shown below.
Select all expressions that are equal to 3⋅3⋅3⋅3⋅3.
3^5
3^4 ⋅ 3
5 ⋅ 3
5^3
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3=\bf9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9=\bf81}\\\\\mathsf{81\times3=\bf result}\\\\\mathsf{= \bf \underline{243}}\large\checkmark[/tex]
[tex]\text{Option A. }\downarrow\\\mathsf{3^5}\\\\\mathsf{3^5= 3\times3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3 = 9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9 = 81}\\\\\mathsf{81\times3= 243}\\\\\large\text{\bold{Option A.} could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option B. }\downarrow\\\mathsf{3^4\times5}\\\mathsf{3^4 = 3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3}\\\\\mathsf{3\times3=9}\\\\\mathsf{9\times9= 81}\\\\\mathsf{81\times3=243}\\\\\large\text{Option B. could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option C. }\downarrow\\\mathsf{3\times5}\\\\\maths{3+3+3+3+3}\\\\\mathsf{3+3=6}\\\\\mathsf{6+6+3}\\\\\mathsf{6+6=12}\\\\\mathsf{12+3=15}\\\\\mathsf{15\neq243}\\\\\large\text{Option C is NOT your ANSWER}[/tex]
[tex]\text{Option D.}\downarrow\\\mathsf{5^3}\\\\\mathsf{5^3=5\times5\times5}\\\\\mathsf{5\times5\times5}\\\\\mathsf{5\times5=25}\\\\\mathsf{25\times5 = 125}\\\\\mathsf{125\neq243}\\\\\large\text{Option D. is NOT your ANSWER}[/tex]
[tex]\boxed{\boxed{\large\text{Answers: \boxed{\boxed{\mathsf{\bf{Option\ A.)\ 3^5 \ \& \ Option\ B.)\ 3^4 \times 3}}}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
A) 3^5 B) 3^4*3
Step-by-step explanation:
Help and show work please
Answer:
11111111 111 1 1 1 11
Step-by-step explanation:
Answer:
ok 1+1= 25 and add 3000 and you get 1
Step-by-step explanation:
PLS HELP!!
Figure ABCD has vertices A(1, 1), B(1, 4), C(4,4), and D(4,1). What are the coordinates of the vertices of Figure
A'B'C'D' after a reflection across the line x = -2 and a translation 3 units up? Drag numbers to complete the coordinates.
Numbers may be used once, more than once, or not at all.
-
numbers are -8,-7,-6,-5,-4,4,5,6,7,8
Answer:
A’ (-5,4) B’ (-5,7), C’ (-8,7), D‘ (-8,4)
Step-by-step explanation:
Just had this test lol
Keeping it simple by asking for more help. Question 10.
Answer: I will go with A or you can choose d if you want
Step-by-step explanation:
How do you find the slope to (3,12),(3,-17)
Answer:
you plot them together
1. draw a t shape and then plot it like x then y
Answer:
trust your instincts
Step-by-step explanation:
decide on your own destiny i can not interfeir
Nick went canoeing on the river he traveled 1 mile in 17 minutes.at this rate,how far will he travel in an hour and 25 minutes
9514 1404 393
Answer:
5 miles
Step-by-step explanation:
An hour and 25 minutes is 85 minutes. Using the given information we can find the distance d with the proportion ...
[tex]\dfrac{\text{distance}}{\text{time}}=\dfrac{d}{85\text{ min}}=\dfrac{1\text{ mi}}{17\text{ min}}\\\\d=\dfrac{85\text{ min}}{17\text{ min}}(1\text{ mi)}\qquad\text{multiply by $85$ min}\\\\d=5(1\text{ mi})\qquad\text{simplify}\\\\d=\boxed{5\text{ mi}}[/tex]
In 1 hour and 25 minutes, Nick will travel 5 miles.
Help me this math problem
Let f(x) be the trigonometric function f(x)=sin(x).
On the interval [0,2π), the maximum value(s) of f(x) occur(s) at what x-value(s)?
Answer:
im on a chalange
Step-by-step explanation:
please choose someone else i have 1 day to do this
Please help me I wanna go to sleep
What is true about this sequence?
8000, 4000, 2000, 1000, ...
Answer:
B
Step-by-step explanation:
each consecutive term is divided by 2
A rectangular city park is 6/8 mile long the park has an area of 1/4 Mile2. What is the width of the park?
I need an answer! Please!
Answer:
The answer is 1/3
Step-by-step explanation:
divide 6/8 and 1/4 and you will get 1/3
The sector of a circle has an area of 104pi/9 square inches and a central angle with measure 65 degrees. What is the radious of the circle in inches? Show work. a. 5.7 b. 8 c. 64 d. 104
Answer: b. 8
Step-by-step explanation: I don’t have work
The radius of the circle in inches should be considered as the 8 when the measurement of the central angle is given.
Calculation of the radius of the circle;Since
The sector of a circle has an area of 104pi/9 square inches and a central angle with measure 65 degrees.
Also we know that
Area of the sector = [tex]65 / 360 *[/tex] Area of circle
[tex]104\pi \div 9 = 65\div 360 (\pi r^2)\\\\104\div 9 = 65\div 360 r^2\\\\[/tex]
r = 8
Hence, The radius of the circle in inches should be considered as the 8.
Learn more about circle here: https://brainly.com/question/15593101
What is the value of k if (1, 1) is a solution of 2x + 7y=k?
(ab)(6a^5b)(-ab) simplified please
Answer:
25b3a+93b+60a=30a2+b2
Step-by-step explanation:
There are 12 counters. One third of the counters are yellow. How many counters are yellow?
Answer:
I think 4
Step-by-step explanation:
1/3 is how many are yellow. so if u do 12/3=4
Answer:
4
Step-by-step explanation:
1/3 is equivalent to 4×1 and 2/3 is equivalent to 4×2 and 3/3 is equivalent to 4×3 which equals 12 so there are 4 counters that are yellow.
complete the table by supplying the measure of inscribed angle and its intercepted arc
Answer/Step-by-step explanation:
Based on the inscribed angle theorem, any inscribed angle = ½ of its intercepted arc
Thus:
✔️Inscribed angle = 57°
Intercepted arc would be: 2*57 = 114°
✔️Intercepted arc would be: 123°
Inscribed angle = ½(123) = 61.5°
✔️Intercepted arc would be: 46°
Inscribed angle = ½(46) = 23°
✔️Inscribed angle = 69°
Intercepted arc would be: 2*69 = 138°
✔️Intercepted arc would be: 155°
Inscribed angle = ½(155) = 77.5°
The Property where if the order of addends changes, the sum stays the change
How is basic math used in a business? Give me three examples.
Answer:
Understanding basic business math is necessary for profitable operations and accurate record keeping. Knowing how to add, subtract, multiply, divide, round and use percentages and fractions is the minimum you need to price your product and meet your budget.
Please help please please plewse
Answer:
-1 and -5
Step-by-step explanation:
Please help ..........
How do you simplify 32/48
Answer:
2/3
Step-by-step explanation:
divide numerator and denominator by 16
32÷16=2
48÷16=3
answer is 2/3
Thus, 2/3 is the simplified fraction for 32/48 by using the GCD or HCF method. Thus, 2/3 is the simplified fraction for 32/48 by using the prime factorization method.
hottest centralisation
Answer:
centralisation mean a direction explain that we often a high how well we cancan predict future actions of others.
Step-by-step explanation:
work out the value of angle x 62 degrees
Answer:
180- (62*2)= x( angles opposite to equal sides)
180-124= x
x= 56
Step-by-step explanation:
Be Strong Now, Because Things Will Get Better. It Might Be Stormy Now, But It Can't Rain Forever.
Answer:
aw ty but is there a question?
Step-by-step explanation:
If you were to calculate the average rate of change of a function over a variety of intervals and you found that they were all the same, what conclusion could you draw and why
2 3/4 yards of fabric for $22 express as unit rate. round to nearest cent if necessary
Answer:
7
Step-by-step explanation:
Answer:
13(rounded) cents per 1/4 yard and 50 cents per yard
Step-by-step explanation:
Step 1: Convert the mixed fraction into an improper fraction
[tex]2\frac{3}{4} = \frac{4}{4}+\frac{4}{4}+\frac{3}{4}[/tex]
[tex]2\frac{3}{4}=\frac{11}{4}[/tex]
Step 2: Find the unit price per 1/4 yard
[tex]\frac{11}{4}/22[/tex]
[tex]0.125 = 13 \ cents[/tex]
Step 3: Find the unit price per 1 yard
[tex]12.5\ cents\ per\ 1/4\ yard=50\ cents\ per\ 1\ yard[/tex]
Answer: 13(rounded) cents per 1/4 yard and 50 cents per yard