A school has found from past records that the average scores for boys is 75 in a sample of 45 boys, and the average scores for girls is 85 in a sample of 30 girls. The population standard deviations for boys' and girls' scores were 25 and 17, respectively. The 90% confidence interval for the difference of the population means is approximately (_____, −2.022). Assume that the distributions of the scores of men and women are normally distributed. Round your answer to two decimal places.
Confidence Level Corresponding zc Value
90% confidence zc=1.645
95% confidence zc=1.96
99% confidence zc=2.576
Answer:
The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Boys:
Mean of 75, sample of 45, standard deviation of 25.
This means that [tex]\mu_B = 75, s_B = \frac{25}{\sqrt{45}}[/tex]
Girls:
Mean of 85, sample of 30, standard deviation of 17.
This means that [tex]\mu_G = 85, s_G = \frac{17}{\sqrt{30}}[/tex]
Distribution of the difference of mean grades of boys and girls:
[tex]\mu = \mu_B - \mu_G = 75 - 85 = -10[/tex]
[tex]s = \sqrt{s_B^2+s_G^2} = \sqrt{(\frac{25}{\sqrt{45}})^2+(\frac{17}{\sqrt{30}})^2} = 4.85[/tex]
Confidence interval:
As stated, the critical value is [tex]z = 1.645[/tex]
The margin of error is of:
[tex]M = zs = 1.645*4.85 = 7.98[/tex]
Lower bound:
[tex]\mu - M = -10 - 7.98 = -17.98[/tex]
Upper bound:
[tex]\mu + M = -10 + 7.98 = -2.02[/tex]
The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).
Can anyone please help me with this? i need answers for all the blank spaces. I dont need to know how to do it, just the answers.
Answer:
[tex]\\(x- -1)^{2} + (y- -1)^{2} = 13[/tex]
so, -1, -1 and 13
Pls help I’ll brainlest and add extra points asap
Step-by-step explanation:
1. E
2. G
3. I
4. J
5. H
6. F
7. A
8. D
9. B
10. C
The Unit Circle
Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary, round your results to the nearest hundredth.
29°
a. (0.87, 0)
b. (0.87, 0.48)
c. (0.48, 0.87)
d. (1, 0.48)
Please select the best answer from the choices provided
Answer:
B. (0.87, 0.48)
Step-by-step explanation:
I calculated it logically
NEED THE AGE OF HIDE
Situation: A farmer in China discovers a mammal hide that contains 37% of its original amount of C-14. N = Noe No = inital amount of C-14 (at time t = 0) N = amount of C-14 at time t k = 0.0001 t = time, in years
Answer:
54678 years
Step-by-step explanation:
Mitch jarred 12 liters of jam 2 days. How many days does Mitch need to spend making jam if he want to jar 18 jam in all
Answer:
3 days
Step-by-step explanation:
well, in 2 days mitch can jar 12 liters of jam right? but 12 is divisible by 2. so let’s just do that to help us out later, 12 / 2 = 6
now that we have that, let’s make sure. in 1 day he can jar 6, in 2 he can jar 12.
that seems right! so now, can we add 6 to 12 to make 18? yep! how many more times do we need to add 6? 1 time. so 12 + 6 = 18. every 6 liters is 1 day. so 1 day + 1 day + 1 day (18 liters) is 3 days total!
hope this helped you!
Daniel is very extraverted.He admits that he is not comfortable unless surrounded by other people,and he energetically pursues activities that require the company of others.His cousin Bill,about the same age,is very introverted.Bill is self-reflective and prefers more solitary pursuits.Regardless of their personality characteristics,which of the following is likely to contribute most to their long-term happiness?
A) They are good friends who are willing to help each other in difficult times.
B) They bought a lottery ticket together and were lucky enough to win a huge jackpot.
C) They both have jobs that require very little effort.
D) They both have very few responsibilities and are careful to avoid committing themselves to any community service.
Answer:
A is the most likely answer
Step-by-step explanation:
but how is this a math question?
A line has a slope of -5 and has a point of (-2,2) and (-1, -3). Write the equation for the line in slope intercept form.
9514 1404 393
Answer:
y = -5x -8
Step-by-step explanation:
The y-intercept can be found from ...
b = y -mx
Using the first point, we have ...
b = 2 -(-5)(-2) = -8
Then the slope-intercept equation is ...
y = mx + b . . . . . . . . for slope m and y-intercept b
y = -5x -8
Answer:
the answer is
y=-5×-8
Step-by-step explanation:
:))
Nina purchases a gallon of milk for $3 and some tomatoes for $2 per pound
from the grocery store. Which equation represents the relationship
between the number of poundsp of tomatoes purchased and the total
amount x Nina spent at the grocery store? *
Answer:
x = 3 + 2p (2p is 2 times p)
A model rocket is launch from a platform 17 feet high in the initial velocity is 40 ft The path of the rocket is modeled by the equation 16x^2 +40X +17=0 When does the rocket land
Answer:
It will be in the air until P(x) is zero.
P(x) = -16x2 + 32x = -16x(x - 2)
P(x) = 0 ⇒ x = 0 or x = 2
It starts on the ground at x = 0, so the total time in the air must be x = 2 seconds.
17. Calculate the profit and loss percent if CP is RS 480 andSP is RS420
Answer:
there is no profit there is loss because CP is greater than SP
Step-by-step explanation:
loss=CP-SP
=Rs480-Rs420
=Rs60
loss%=loss/cp*100%
=60/480*100%
=6000/480
=12.5%
Identify all of the transformation effects on the graph of the function f(x) = x when f(x) is replaced with -f(x + 4) - 6.
A)
shifted up 6 units
B)
shifted down 6 units
shifted left 4 units
D)
shifted right 4 units
E)
reflected over x-axis
Answer: B,C E put as brainliest
Step-by-step explanation:
PLEASE HELP!! Find mCFD
180°
276
307
53°
Answer:
307°
Step-by-step explanation:
CF is a diameter of the circle. so, any arc connecting C and F has an arc angle of 180° (half-circle).
so, we need to add the arc angle FD.
we know the arc angle ED = 79°.
so, what is left to add is the arc angle FE.
the arc angle FE is the same as BC.
and the arc angle BC is the supplementary angle (means together they have 180°) to 132° :
BC = 180 - 132 = 48°
therefore,
the arc angle CFD = 180 + 48 + 79 = 307°
What will be the coordinates of the image after a translation up 4 units and right 6 units
Answer:
B
Step-by-step explanation:
To find the answer, translate each point and then use the process of elimination.
For the first point, the coordinates are (-4, -2). The -4 is x and the -2 is y. Translations up and down relate to the y value, while translations left and right relate to x. To translate up 4 units, add 4 to the y value of the coordinate. -2 + 4 is 2, so the y coordinate of the first point will be 2. That eliminated A and D.
For the second point, translate up 4 units (-5 + 4) and you get -1. So the y value of the second point will be -1. In option C, it is positive 1. So that leaves only B.
plzzzzzzzz help for a brainly
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
2 ft
1 ft
2 ft
Answer:
V=lwh /3
Step-by-step explanation:
Consider the following graph of y = f (x). I need help
Answer:
A.) 1 and 5
B.) -3
C.) [-1, 6]
D.) [-3, 2]
I don't know what E is
Step-by-step explanation:
Find the missing side of each right triangle (Pythagorean’s #Theorem)
Answer:
3
Step-by-step explanation:
The formula for the Pythagorean's Theorem is a^2 + b^2 = c^2, so first you know that hypotenuse is the longest side or the opposite side from which the right angle is which in this case is the 6 so you are looking for a leg rather then the hypotenuse which means we are going to be doing subtraction.
a^2 + b^2 = c^2
√27^2 - b^2 = 6^2
27 - b^2 = 36
-27 -27
b^2 = 9
b^2 = √9
b = 3Is the answer yes or no?
Answer:
yes
Step-by-step explanation:
because in order to create a right triangle all of its sides must be different
Answer:
Yes
Step-by-step explanation:
Using the Pathagerum theorm (C**2 = A**2 + B**2)
The hypotinuse as always the longest side except for an equal lateral triangle. So if it is a right angle triagle so if true then,
13**2 = 5**2 + 12**2
169 = 25 + 144
169 = 169
so it is true (YES).
How find the length of a hypotenuse triangle
Answer:
Step-by-step explanation:
A hypotenuse is calculated on a triangle with a right angle. The hypotenuse is the side opposite the sides with the right angle. The equation is a^2 + b^2=c^2 where the hypotenuse is the square root of c.
Jonathan's preschool class has 9 girls and 6 boys. Which properties can be used to determine the percent, p, of boys in the class?
addtion
becuase when you add the number of boys and girls together you get the overall number of the class.
Answer: properties would be multiplication and the answer would be 40%
Step-by-step explanation: You can use cross multiplication to identify the answer to this.
[tex]\frac{6}{15}[/tex] --> [tex]\frac{x}{100}[/tex]
Help me with this.thank you
Answer: 3 miles.
Step-by-step explanation:
Since we are given the information that Ms. Wilson walked ¾miles each day. To calculate the total distance that Ms. Wilson will walk for 4 days, we have to multiply the distance walked each day by 4.
This will be:
= ¾miles × 4
= 3 miles
Therefore, Wilson walked a distance of 3 miles for the 4 days.
An election ballot asks voters to select four city commissioners from a group of fourteen candidates. In how many ways can this be done ?
Fifty seven percent (57%) of the students applying to a university are accepted. In other words, there is a 57% probability of being accepted. A sample of 12 applicants has been selected. Using Excel, answer the questions below. Please, round your solutions to 4 decimal places (if your answer has less than 4 decimals, it is okay to leave it as it is).
please help will give brainliest !!
Complete the following Truth Table
p q r ~p ∧ ~q ∨ r
T T T (a)
T T F (b)
T F T (c)
T F F (d)
F T T (e)
F T F (f)
F F T (g)
F F F (h)
The inside diameter of a randomly selected piston ring is a normally distributed random variable with mean 12 cm and standard deviation 0.04 cm. (a) What is the diameter that is exceeded by only 5% of the piston rings
Answer:
[tex]x=12.07[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =12cm[/tex]
Standard deviation [tex]\sigma=0.04[/tex]
Significance level [tex]\alpha=5\%=0.05[/tex]
Therefore
Confidence level [tex]95\%=0.95[/tex]
From table [tex]P(z<1.645)=0.95[/tex]
Generally the equation for Z-score is mathematically given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]x=z\sigma+\mu[/tex]
[tex]x=1.645*0.04+12[/tex]
[tex]x=12.07[/tex]
Alex is making a blanket for her nephew. The blanket has a length of 5 ft and a width of 4 ft. She is going to sew ribbon edging around the perimeter of the blanket. The edging costs $3 per yard. How much will it cost for Alex to get the amount of ribbon edging that she needs? Help Resa 5 ft Skip 4 ft 4 ft 5 ft HINT: There are 3 feet in one yard.
She will need 6 yards. the permiter is 16 which 5 wouldnt be enough
A mechanic repaired 12 cars one day,
but the next day they repaired 7 cars.
What was the percent change?
Answer:
78
Step-by-step explanation:
when there is a five car diffrence its possible
Based on the graph, how many distinct real number solutions does the equation x3 – 3x2 + 4 = 0 have?
Answer:
2 solutions
-1 and 2
Step-by-step explanation:
Solve the following quadratic function by utilizing the square root method. f(x) = 1 - x2 x = + [?]
Answer: 1
Step-by-step explanation:
If x = 0
then, f(x) = 1 - 0
f(x) = 1
x = ±1
Let f(x)=0
1-x²=0-x²=-1x²=1x=±1