Answer:
true
Step-by-step explanation:
An experiment on the teaching of reading compares two methods, A and B. The response variable is the Degree of Reading Power (DRP) score. The experimenter uses Method A in a class of 100 students and Method B in a comparable class of 100 students. Students are assigned to the two classes at random. Suppose that in the population of all children of this age the DRP score has the N(75, 30) distribution if Method A is used and the N(74, 40) distribution if Method B is used. Let us call the mean DRP score for 100 students in the A group. Let us call the mean DRP score for 100 students in the B group ý.
Required:
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
Answer:
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables:
Normal probability distribution
When the distribution is normal, we use 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.
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.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the subtraction of the mean of each variable, while the standard deviation is the square root of the sum of each variance.
Method A:
One student: N(75,30), so [tex]\mu = 75, \sigma = 30[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{30}{\sqrt{100}} = 0.3[/tex]
Method B:
One student: N(74,40), so [tex]\mu = 74, \sigma = 40[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{40}{\sqrt{100}} = 0.4[/tex]
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
This is the probability that B - A >= 5. So
[tex]\mu_{B-A} = \mu_B - \mu_A = 74 - 75 = -1[/tex]
[tex]s_{B-A} = \sqrt{s_A^{2}+S_B^{2}} = \sqrt{(0.3)^2+(0.4)^2} = 0.5[/tex]
We have to find 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - (-1)}{0.5}[/tex]
[tex]Z = 12[/tex]
[tex]Z = 12[/tex] has a pvalue of 1
1 - 1 = 0, so
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
Determine the volume of a sphere with a diameter of 70 mm.
Question options:
A)
3,216.9 mm3
B)
100,024 mm3
C) CORRECT ANSWER
179,594.4 mm3
D)
21,714.7 mm3
Answer:
c.
Step-by-step explanation:
4/3 pi r²
4/3 × 3.142 or 22/7 × 3.5²
You buy rice at $0.71 a pound. One batch of fried rice requires 9 pounds of rice. How much does the rice for one batch cost? Round to the nearest cent.
Answer:
$6.39
Step-by-step explanation:
b= batch
1b=$0.71
9b=?
9b=9($0.71)
9b=$6.39
Nature's Squeeze is a drink stand known for its fresh-squeezed juices. Colin just got his first job working there! During his training, he made 4 drinks in 12 minutes. Today is Colin's first shift, and he will work for 90 minutes.
If Colin makes drinks at the same rate, how many drinks will he make today?
Answer: 30 drinks
Step-by-step explanation:
From the question, we are informed that Colin made 4 drinks in 12 minutes during his training. This shows that a drink is made in (12/4) = 3 minutes.
Since he will work for 90 minutes, the number of drinks that he will make will be:
= 90/3
= 30 drinks
-1+5.8x=1-(9.1x+10)+8.5x solve for x
Answer:
ehjrbbvhbvebvuhbdhvhdhsduhsdbrhw
Step-by-step explanation:
find the slope of the line. (1,1) ,( 3,5)
Answer:
m=2
Step-by-step explanation:
5-1/3-1
4/3-1
4/2
2
I hope this helps
In a shop, a TV has a normal price of £500
The shop has a sale.
On Monday, the normal price of the TV is reduced by 1/10 to give the sale price.
On Tuesday, the sale price of the TV is reduced by 20%
Chris wants to buy the TV.
He has £400 to spend on the TV.
Does Chris have enough money to buy the TV on Tuesday?
Answer:
400> 360
Step-by-step explanation:
1/10 X 500 = 50
500 - 50 = 450
10% = 450/ 10 = 45
20% = 45 x 2 = 90
450 - 90 = 360
Chris does have enough 400> 360
which properties justify the steps taken to solve the system 4x + 3y =25 2x + 5y=19
Answer: we multiply the second equation by -2. This property is the multiplication property of equality (1).
Then, we add the two equations generated. (2) addition property of inequality.
Next, we divide both sides of the equation by 13. That is division property of inequality.
Moreover, we substitute the value obtained for y in the first equation. This is substitution property of equality.
Then, we simplify
Next, we add +3 to both sides of the equation in order to have an equation with only one side having a variable. That is addition property of equality.
Lastly, we divide both sides of the equation by 4. This is division property of equality.
Step-by-step explanation:
Which of the following is the equation for the line of symmetry in this figure?
Can someone help please!
Answer:
X=3
Step-by-step explanation:
3 is in the middle of the figure.
I hope this helps!
to ride a horse at the state fair costs 2$ per minute. Pablo buys a 16 minute ride. Next time her plans to ride 25% longer. How much will he pay?
Help please i will reward brainly
Answer:
40 dollars
Step-by-step explanation:
25% of 16 minutes is 4 mins. 16+4=20 mins.
so 20*2=40 dollars
5 point
Aaron has $36.00 from doing yard work. He gave 1/4 of his $36.00 to his
brother Ryan. How much of his money is still leftover?
Answer:
$27 is left over.
Step-by-step explanation:
If you divide 36 by 4, you can find out what 1/4 of 36 is. 36/4 = 9
This $9 is how much he gave away to his brother. In order to find out how much he has leftover for himself, subtract the $9 from the $36.
36-9 = 27.
Therefore, Aaron has $27 leftover for himself.
whats the answer to -6 = 3/2z
Answer:
Step-by-step explanation:
-6=3/2z
-12z=3
z=-4
.
Simplify the expression below.
1/2x²+2+1/4x+8
plz help
Answer:
[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]
Step-by-step explanation:
[tex] \frac{1}{2} {x}^{2} + 2 + \frac{1}{4} x + 8[/tex]
[tex]2 + 8 = 10[/tex]
[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]
Suppose Gil can write a poem in 1 hour, Holly can write a poem in 2 hours, and Ivan can write a poem in 3 hours. Each person spends 12 hours per day writing poems and requires a wage of $10 per hour to do so. If a literary magazine needs one poem, how much will it cost
Answer:
The literary magazine must pay $ 10 if poem is written by Gil, $ 20 if poem is written by Holly and $ 30 if poem is written by Ivan.
Step-by-step explanation:
The wage indicate the amount of money earned in hour for production of poems. If a literary magazine needs just one poem, then the cost will be the wage multiplied by time taken for the creation of the poem. There are three possibilities:
Gil
[tex]C = \left(10\,\frac{USD}{h})\cdot (1\,h)[/tex]
[tex]C = 10\,USD[/tex]
Holly
[tex]C = \left(10\,\frac{USD}{h}\right)\cdot (2\,h)[/tex]
[tex]C = 20\,USD[/tex]
Ivan
[tex]C = \left(10\,\frac{USD}{h}\right)\cdot (3\,h)[/tex]
[tex]C = 30\,USD[/tex]
The literary magazine must pay $ 10 if poem is written by Gil, $ 20 if poem is written by Holly and $ 30 if poem is written by Ivan.
Darrion's car has a gas mileage of 30 miles per gallon. How many miles can Darrion travel on 13 gallons of gas?
Solve w=3/7(ay+m) for y
Answer:gd
Step-by-step explanation:
Vygfy
Answer:
y = (7w - 3m) / 3a
Step-by-step explanation:
w = 3/7ay + 3/7m
multiply each side by 7 to eliminate fractions
7w = 3ay + 3m
3ay = 7w - 3m
y = (7w - 3m) / 3a
If a tree in a 1 in.: 5ft scale drawing is 12 inches tall, how tall is the actual tree?
10 to the 8 power is what
Answer:
it is 100000000 i think i am not sure either
Find the missing value.
K
N
75°
L
M
Answer:
N
Step-by-step explanation:
Yeah cos it's like n ya know ueuehd
Simplify the following expression:
5(2x-4)-4(2-5x)
Answer:
30x - 28
Step-by-step explanation:
distribute
5(2x) - 5(4) -4(2) - 4(-5x)
10x - 20 - 8 + 20x
30x - 28
Question 6
<
Match the name of the sampling method descriptions given.
Situations
pulling 50 names from a hat
MI divide the population by age and select 5 people from each age
Vask all the students in your math class
Mi call every 15th phone number on every 5th page of the phone book
Sampling Method
a. Stratified
b. Systematic
c. Simple Random
d. Convenience
Answer:
C.
Step-by-step explanation
shes pulling RANDOM names. key word random, hope this helped
Percents can be expressed as fractions and decimals. A percent means “out of 100,” so we can express 40% as the fraction 40⁄100. We can simplify this fraction to2⁄5 by dividing by the greatest common factor, 20.
We can also express a percent as a decimal. Percents show a part out of a hundred, or hundredths, so you can divide the percent by 100 to find the decimal. 40 divided by 100 equals 40 hundredths, or .4. You can also divide the numerator by the denominator in the simplified fraction, 2⁄5, to find the equivalent decimal.
These values are all equivalent.
75% =
A
75/10
B
2/3
C
3/4
D
3/5
Answer:
Definitely 3/4!
Step-by-step explanation:
Option A = 7.5
Option B = 66.6%
Option C = 75% (because 25 times 4 is equal to 100%, so 25 times 3 would be 75)
Option D = 6/10 or 60%
The values that are equivalent to 75% are A) 75/100 (0.75) and C) 3/4.
To determine whether these values are equivalent, let's evaluate each expression and compare the results.
A) 75% can be written as a decimal by dividing 75 by 100:
75% = 75/100 = 0.75
B) 2/3 is already in fractional form and cannot be simplified further.
C) 3/4 is also in fractional form and cannot be simplified further.
D) 3/5 is in fractional form and cannot be simplified further.
Now let's compare the decimal equivalents:
0.75 = 75/100
2/3 = 0.666...
3/4 = 0.75
3/5 = 0.6
Comparing the decimal values, we can see that A) 0.75 and C) 0.75 are equivalent, as they both represent 75% in decimal form.
However, B) 2/3 and D) 3/5 do not equal 0.75 and are therefore not equivalent to 75%.
Hence, the values that are equivalent to 75% are A) 75/100 (0.75) and C) 3/4.
Learn more about Percents click;
https://brainly.com/question/31323953
#SPJ6
Need help finding angle A,B,C,D!!
Solve for R:
r +15/-7=-2
Answer:
1/7
one over seven
Step-by-step explanation:
What is the definition of Antigen?
Please help
Answer:
a toxin or other foreign substance which induces an immune response in the body, especially the production of antibodies.
Evaluate 4 ^ x for (a) x = - 2 and (b) x = 3 . Write your answers in simplest form
The value of 4ˣ for x = -2 and x = 3 is 0.0625 and 64 respectively.
What is an exponential function?The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given function 4ˣ
when x = -2
4ˣ = 4⁻²
using a⁻ⁿ = 1/aⁿ
4⁻² = 1/4² = 1/16
4⁻² = 0.0625
and x = 3
4ˣ = 4³
4³ = 4 x 4 x 4 = 64
Hence the values are 0.0625 and 64 for x = -2 and 3.
Learn more about exponential function;
https://brainly.com/question/14355665
#SPJ5
The Commutative Property states that the order of terms in an expression does not affect the outcome. Which of the following operations does the Commutative Property apply? select all that apply
A. addition
B. subtraction
C. multiplication
D. division
Jana paid an initial fee of $75 to join a fitness gym. She pays $15 per month for her membership. How many months did she have the membership if she spent a total of $255.
asap ill give brainlyist
Answer:
12 months
Step-by-step explanation:
Set up a formula; 75 + 15x = 255
Now, solve for x, which is number of months.
subtract 75 from both sides.
15x = 180
divide both sides by 15.
x = 12
x is equal to 12 - she would have had to have the subscription for 12 months to spend 255$.
what is 729 : 4 in long division
Answer: Here's what I got:
Step-by-step explanation:
I don't know if this what you wanted:
Find the equation of the line thank you
Answer:
y=3/4x-2
Step-by-step explanation:
Answer:
y=3/4x-2
Step-by-step explanation:
y-intercept: -2
slope: 3/4
