Answer:
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between 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.
A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.
This means that:
[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]
An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.
This means that:
[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]
Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Mean:
[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]
Standard deviation:
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
So
[tex]M = 1.645*2.6 = 4.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7
The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
Nadia compares the weights, in grams, of some apples and oranges. She finds the median and interquartile range of the weights. Median Interquartile range (IQR) Apple sample 150 8 Orange sample 130 11 Answer the questions to compare the centers and variabilities of the samples. 1. Which sample has a greater typical value, or median? Write your answer in the space below. 2. Which sample has a greater variability, or spread? Write your answer in the space below. 3. According to these measures, is it possible that the heaviest piece of fruit in the two samples was an orange? Explain why or why not.
Answer:
The higher the interquartile range the bigger the variance as it the difference between the 0.25 and 0.75 quantiles. which basically means if the difference between the 25 percent and 75 percent is higher then there is more variety as they are further away.
Step-by-step explanation:
Which basically means if the difference between the 25 percent and 75 percent is higher then there is more variety as they are further away.
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The apple sample has a greater typical value or median.
The orange sample has a greater variability or spread.
No, it is not possible that the heaviest piece of fruit in the two samples was orange because the median weight of the orange sample is less than the median weight of the apple sample.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
1.
The apple sample has a greater typical value or median, which is 150 grams, compared to the orange sample which has a median of 130 grams.
2.
The orange sample has a greater variability or spread as indicated by the interquartile range (IQR) of 11 grams, which is larger than the IQR of the apple sample which is 8 grams.
3.
No, it is not possible that the heaviest piece of fruit in the two samples was orange because the median weight of the orange sample is less than the median weight of the apple sample.
The median is a measure of central tendency and it indicates that at least half of the oranges weigh less than 130 grams, while at least half of the apples weigh more than 150 grams.
Therefore, it is more likely that the heaviest piece of fruit is an apple, not an orange.
However, we cannot be certain about this without knowing the actual weights of all the apples and oranges in the samples.
Thus,
The apple sample has a greater typical value or median.
The orange sample has a greater variability or spread.
No, it is not possible that the heaviest piece of fruit in the two samples was orange because the median weight of the orange sample is less than the median weight of the apple sample.
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A right rectangular prism has a base with sides 6 cm and 8 cm. If the volume of the prism is 624 cm^3, find the height of the prism.
Answer:
H=13cm
Step-by-step explanation:
Volume=Length x Width x Height
V=624cm^3
L=8cm
W=6cm
8cm x 6cm= 48cm^2
624cm^3 divided by 48^2= 13cm
H=13cm
Hope this helps!
The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price.
What was the sale price of the skateboard?
Answer:
The sale price was $67.20
Step-by-step explanation:
The sale price is 30% less than the original price. Symbolically,
Sale price: (100% less 30%) of $96, or
(1.00 - 0.30)($96), or 0.70($96) = $67.20
The sale price was $67.20
what is the solution to the system?
y = 5x
y = 2x - 9
Find A UB.
A)
{3,7)
B)
{3,5,6,7}
{2,3,5,7,8,9,12}
D)
{3,5,6,7,8,11,12}
Answer:
D
Step-by-step explanation:
3,5,6,7,8,11,and 12
Because that's the union
The slope of the line below is 1.5. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(4,3)
Answer:
[tex] y - 3 = 1.5(x - 4) [/tex]
Step-by-step explanation:
Given:
Slope = m = 1.5
Coordinates of labelled point = (a, b) = (4, 3)
Point-slope equation takes the form of [tex] y - b = m(x - a) [/tex].
Therefore, to write the equation, substitute a = 4, b = 3 and m = 1.5 into [tex] y - b = m(x - a) [/tex].
Thus:
[tex] y - 3 = 1.5(x - 4) [/tex]
Carlos is studying a cell under a microscope. He observes the structure
that allows things in and out of the cell. What is this called? *
Cell membrane
Cytoplasm
Chlorplasts
Nucleus
answer the question
A.2
B.7
C.13
D.22
Sam picks corn on his uncle's farm. His uncle pays him $0.40 per basket for the first 50 baskets of corn that he picks in a day and $0.50 per basket for all baskets picked over 50. On Friday Sam picked 120 baskets of corn. How much did he earn?
Answer:
$55
Step-by-step explanation:
Find out the number of baskets paid at $0.5/basket:
Since the first 50 are paid for $0.4, and he picked 130 baskets, we can subtract 50 from 120, giving us 70.
Finding the amount paid at $0.4/basket:
50*$0.4 = $20
Finding the amount paid at $0.5/basket:
70*$0.5 = $35
Total = $55
so much more. Si se congres
ES
Evaluate this expression 30 - (2 x 3 + 10) + 4 + 32
Answer:
50
Step-by-step explanation:
parentheses...2×3=6...6+10=16
30-16+4+32
50
Put =, >, or < between
-0.171100011 _____ -0.171100010
Answer:
Put "<" between -0.171100011 _____ -0.171100010
Step-by-step explanation:
-0.171100010 is greater than -0.171100011 because they are negative numbers so -0.171100011 is further than -0.171100010 to 0, therefore -0.171100010 is greater.
Mark brainliest if this helped :)
Use words to explain how to multiply (3^3) (3^4).
Pls help
Answer:
9^7
Step-by-step explanation:
Multiple the two 3's and get 9 then when you multiply exponents you add them and get 7
-3, 7 THOSE NUMBERS CUT OFF
WILL GIVE BRAINLIST
Answer: +3
Step-by-step explanation:
5 + (-2) ( + × - = - ) ∴ 5 - 2 = 3
Find the coordinates of point B on AC such that AC is 6 times long as AB.
Answer:
I think it's 36 I'm not sure because you did give me more to go off of to help you sorry if it's wrong
Please help ASAP Please
Answer:
72 in.
Step-by-step explanation:
The height is scaled up time 6, so the base would be too. 12*6 = 72.
If 3 candy bars cost $2.70 at the gas station mart. What is the cost for 1 candy bar?
The image is below please help I am crying
Answer:
Quadrant III
Step-by-step explanation:
Maddie Evans drove 180 miles in the same matter I'm not detect a turbo propeller plane to travel 690 miles the speed of the plane was 170 mph faster than the speed of the car find the speed of the plane
Answer:
let
m = the speed of Mattie
d1 = 180 mi the distance Mattie traveled
p = the speed of the plane
d2 = 630 mi the distance the plane traveled
the speed of the plane was 150 mph faster than the speed of the car
p = m + 150
since speed = distance/time => time = distance/speed
d1/m = d2/p
180/m = 630/p cross multiply
180p = 630m divide both sides by 90
2p = 7m
by solving the system of equations
p = m + 150
2p = 7m
we find
p = 210 mph
The speed of the plane was 210 mph
x ( x + 4 ) − 3 = 4 ( x + 19.5 )
Answer:
9
Step-by-step explanation:
If
2/9
of an amount is equal to 14, what is the whole amount equal to
I think it’s 63.
I divided to get its simplified version. 14÷2 is seven, which would be 1/9. Multiply the denominator by seven, which is 63. You can also look up online to check that. 14 is indeed 2/9 of 63.
q square =-1 what is q
9514 1404 393
Answer:
±i
Step-by-step explanation:
q² = -1
q = ±√(-1) = ±i . . . . . . i is the name given to the square root of -1.
if f(x) = 1/x^14, what is f'(x)?
Answer:
[tex]f(x) = \frac{1}{ {x}^{14} } \\ f'(x) = - \frac{14}{x {}^{15} } [/tex]
5.
Which value of x would satisfy this inequality?
V3
4
2
A А.
С
D
000
4
10
Answer:
C) 4/5
Step-by-step explanation:
pi/4 = 0.7853981634
[tex]\frac{\sqrt{3} }{2}[/tex] = 0.8660254038
3/4 = 0.75. It's less than pi/4, so not correct
9/10 = 0.9. It's more than 0.866, so not correct
4/5 = 0.8. It's right for both condition
8/9 = 0.888. It's more than 0.866, so not correct.
How many outcomes are there from rolling 3 dice
I'm pretty sure its 24-
but im not completely sure
dice have six sides and you're rolling three times, so three times six- T-T
Answer:
216
Step-by-step explanation:
lots.
You can get any one of 6 results from the first die
You can get any one of 6 results from the second die
You can get any one of 6 results from the third die.
Outcomes = 6 * 6 * 6 = 216. Try list time and you will see that there must be that many.
Suppose the first die is a weighted die such that you always get one.
Suppose the other two dice are fair ones. And they each can be anything.
Those two fair ones will give you 36
Now if you catch on to the way the first die works and trade it for a fair one, you will get 6 times 36 which is 216
Calculate
a) 20% of £150
b) 15% of 80 kg
c) 85% of 2500 m
Answer:
A) 30
B) 12 kg
C) 2,125 m
Step-by-step explanation:
help please!
options are
10.2
17.6
8.8
13.4
9514 1404 393
Answer:
(a) 10.2 ft
Step-by-step explanation:
The total surface area S is the sum of the base area and the lateral area. The base area is the area of the two triangular bases, which have a "base" of 6 ft and a height of 4 ft.
area of 2 bases = 2(1/2)bh = bh = (6 ft)(4 ft) = 24 ft²
The lateral surface area is the sum of the areas of the three rectangular faces. That will be ...
total face area = (4 ft)(x) +(6 ft)(x) +(7.2 ft)(x) = (17.2 ft)(x)
So, the total surface area is ...
200 ft² = 24 ft² + (17.2 ft)(x)
176 ft² = (17.2 ft)x . . . . . . . . . . subtract 24 ft²
(176 ft²)/(17.2 ft) = x ≈ 10.2 ft . . . . . divide by the coefficient of x
The unknown prism height is about 10.2 ft.
{ 2 x [4 - (6 ÷ 2)]} x 3
Answer:
6x^2
Step-by-step explanation:
Answer:
6x²
Step-by-step explanation:
(2x(4 - (6 ÷ 2))) × 3x
(2x(4 - 3)) × 3x
2x(1) × 3x
2x × 3x
6x²
The expected annual demand for the newly approved drug Prisdol is 50,000, but there is a lot of uncertainty. A plant to produce the drug will be built at a cost of $16 per unit of capacity, which is a one-time expense. In addition, there is an annual maintenance cost of $0.40 per unit of capacity. The production cost per unit is $0.20. The drug’s selling price will be $3.70/unit. Suppose that Z denotes the random demand for the drug in a year, and suppose that a plant is built with an annual capacity of 45,000. No inventory will be built up; the company will produce only what is needed for demand in a year, and no more than capacity. Select the least accurate statement regarding elements of a model for this setting.
1 The cost to build the plant is 45,000 * $16.
2 The annual maintenance cost is 45,000 * $0.40.
3 The sales revenue in a year is Z * $3.70
4 The unsatisfied demand in a year is max(Z – 45,000, 0).
Answer:
The least accurate statement regarding elements of a model for this setting is:
4 The unsatisfied demand in a year is max(Z – 45,000, 0).
Step-by-step explanation:
Expected annual demand for Prisdol = 50,000
Annual Plant Capacity = 45,000 units of drugs
Cost of building the plant = 45,000 * $16
Annual maintenance cost = 45,000 * $0.40
Production cost per unit = $0.20
Selling price per unit = $3.70
Sales revenue in a year = Z * $3.70,
where Z denotes the random demand in a year
b) Statements 1, 2, and 3 are accurate in this model setting. However, statement 4 sets up a model that does not concur with the setting. The unsatisfied demand in a year should be Z minus 45,000 if the plant produced full capacity. Otherwise, it is Z minus annual production units.
Which statement is true?
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
Only some squares are rectangles. Rectangles have 4 right angles. Therefore, only some squares have 4 right angles.
All squares are rectangles. Rectangles have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.
Only some squares are rectangles. Rectangles have 4 sides that are the same length. Therefore, only some squares have 4 sides that are the same length.
Answer:
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
All recatangles have 4 angles which are 90°. Though all squares are rectangles, remember, not all rectangle are squares
Hope this helps, Bye!
The true statement is "All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles".
What is a square?That rectangle whose all sides are equal is called a square.
A square has its diagonals perpendicular bisector to each other and is of the same length. (this is actually a characteristic property, which means that if a quadrilateral has its diagonals equal and perpendicular,
then it is a square for sure).
A square is always a rectangle, parallelogram, a rhombus, and a quadrilateral but its reverse statement may or may not be true.
also, it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square.
All squares are rectangles. Rectangles have 4 right angles.
Therefore, all squares have 4 right angles.
All rectangles have 4 angles which are 90°. Though all squares are rectangles, remember, not all rectangles are squares
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