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
What is the value of the following expression when b = -2 and C = 3? -12b + 5c - 15
Answer:
-24
Step-by-step explanation:
12(-2)+5(3)-15
-24+15-15
-24+15
-9-15
= -24
this is confusing, i need help
Answer:
Step-by-step explanation:
2. SV ║TU
3. SV ≅TU
7. corresponding sides of congruent Δ are congruent
8. quadrilaterals that have one set of opposite sides ║ and ≅ are parallelograms
please help mee with this thing
Write the equation of a parabola in vertex form,
f(x) = a(x – h)2 +k, with vertex (-1, 8) and
passing through (3,4)
You must show your work to receive full credit
Answer:
Step-by-step explanation:
Vertex-form equation for a vertical parabola with vertex (h,k):
y = a(x-h)²+k
Plug in coordinates of vertex:
y = a(x+1)²+8
plug in (3,4) and solve for a:
4 = a(3+1)²+8
a = -¼
The equation of the parabola is
y = -¼(x+1)²+8
What is the decimal multiplier to decrease by 0.4%
Answer:
.004
Step-by-step explanation:
translate the percent to a decimal
Answer:
0.996
Step-by-step explanation:
for a decrease u need to transfere to a decimal then take it away from 1
Classify the following triangle. Check all that apply. A. Scalene B. Right C. Acute D. Equilateral E. Obtuse F. Isosceles
Answer:
E and F
Step-by-step explanation:
The triangle given has two equal sides, and an obtuse angle that is more than 90° that measures 120°. The other two angles are of equal measure since their opposite sides are of the same length. Thus, this implies that it is an isosceles triangle because it has two equal base angles and two equal sides. It also implies that it is an obtuse triangle since one of it's angles is more than 90°.
Answer:
the correct answer is acute and scalene
How do I write a polynomial when given the zeros
Answer:
Given the zeros of a polynomial, you can very easily write it -- first in its factored form and then in the standard form. Subtract the first zero from x and enclose it in parentheses. This is the first factor. For example if a polynomial has a zero that is -1, the corresponding factor is x - (-1) = x + 1.
Step-by-step explanation:
This is equation
I don't know how to do
so can anyone tell me plz
with explanation it will help me alot ❤
Answer:
[tex] - \frac{10}{9} [/tex]
Find the value of x.
125°= (5x + 30)
Answer: the answear is 19
Step-by-step explanation:
first you subtract 30 from the 30 and the 125 which takes out the 30 and makes the 125, 95
second you divide 5 by 5 and cross it out
then you divide 95 by 5 and get 19 which is your answer
The manager of a music store has kept records of
The manager of a music store has kept records of the number of CDs bought in a single transaction by customers who make a purchase at the store. The accompanying table gives six possible outcomes and the estimated probability associated with each of these outcomes for the chance experiment that consists of observing the number of CDs purchased by a randomly selected customer at the store.
Number of CDs purchased 1 2 3 4 5 6 or more
Estimated probability 0.30 0.25 0.20 0.15 0.05 0.05
(a) What is the estimated probability that the next customer purchases three or fewer CDs?
(b) What is the estimated probability that the next customer purchases at most three CDs?
How does this compare to the probability computed in part (a)?
greater than part (a)less than part (a) the same as part (a)
(c) What is the estimated probability that the next customer purchases five or more CDs?
(d) What is the estimated probability that the next customer purchases one or two CDs?
(e) What is the estimated probability that the next customer purchases more than two CDs?
Answer:
(a) [tex]P(x\le 3) = 0.75[/tex]
(b) [tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
(c) [tex]P(x \ge 5) = 0.10[/tex]
(d) [tex]P(x = 1\ or\ 2) = 0.55[/tex]
(e) [tex]P(x > 2) = 0.45[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{CDs} & {1} & {2} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.30} & {0.25} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
Solving (a): Probability of 3 or fewer CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
Solving (b): Probability of at most 3 CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
Solving (c): Probability of 5 or more CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {5} & {6\ or\ more}\ \\ {Prob} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x \ge 5) = P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x\ge 5) = 0.05 + 0.05[/tex]
[tex]P(x \ge 5) = 0.10[/tex]
Solving (d): Probability of 1 or 2 CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {1} & {2} \ \\ {Prob} & {0.30} & {0.25} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x = 1\ or\ 2) = P(1) + P(2)[/tex]
This gives:
[tex]P(x = 1\ or\ 2) = 0.30 + 0.25[/tex]
[tex]P(x = 1\ or\ 2) = 0.55[/tex]
Solving (e): Probability of more than 2 CDs
Here, we consider:
[tex]\begin{array}{ccccc}{CDs} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x > 2) = P(3) + P(4) + P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x > 2) = 0.20+ 0.15 + 0.05 + 0.05[/tex]
[tex]P(x > 2) = 0.45[/tex]
Killian has $25 in his bank account. He wants to have at least $100. Working for his dad he earns $7.50 for each hour. Write an inequality that would help you find the number of hours he needs to work.
Answer:
Step-by-step explanation:
100-25<= 7.5x
x >= 10
Answer:
Responsability+nopartyscapes=200$!!!!
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
D
Step-by-step explanation:
How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot.
14.5 ft
15.5 ft
17.0 ft
19.0 ft
Answer:
15.5
Step-by-step explanation:
on edguenity
Answer:
15.5
Step-by-step explanation:
trust
Select the correct answer.
Which of the following tables corresponds to the equation below?
y =
O
A.
I
0
1
3
4
5
y
1
4
16
64
256 1,024
B.
0
1
2
3
4
5
y
0
1
4
16
64
4
0
1
2
3
4
5
4
12 /
1
4
16
64
256
D.
0
1
3
4
y
1
4
8
12
16
+
Answer:
A.
Step-by-step explanation:
The table that corresponds to the equation y = ¹/₄(4ˣ) is; Table C
How to simplify an equation?We are given the equation; y = ¹/₄(4ˣ)
At the input value of x = 0;
x = ¹/₄(4⁰)
x = ¹/₄
At the input value of x = 1;
y = ¹/₄(4¹)
y = 1
At the input value of x = 2;
y = ¹/₄(4²)
y = 4
At the input value of x = 3;
Thus;
y = ¹/₄(4³);
y = 16
At the input value of x = 4;
y = ¹/₄(4⁴)
y = 64
At the input value of x = 5;
y = ¹/₄(4⁵)
y = 256
Read more about Equations at; https://brainly.com/question/2972832
#SPJ6
Need help finding angle A,B,C,D!!
Factor the polynomial completely.
x^4 – 256
Answer:
(x²+16)(X+4)(x-4)
Step-by-step explanation:
x⁴ can be written as (x²)²
256 can be written as (16)²
by identity. a²-b²= (a+b)(a-b) :
(x²+16)(x²-16)
x²-16 can be written as (x)²- 4²
by identity. a²-b²= (a+b)(a-b) :
(X+4)(x-4)
Therefore, the factors altogether would be
(x²+16)(x+4)(x-4)
15j + 15 i need this ASAP will give brainlyest
Answer:
15 ( j + 1)
Step-by-step explanation:
You need to factor it.
15 ( j +1 )
= 15j + 15 ✔
(-1 1/2) * 2/3 =
pls i need help!!
Answer: -1
Step-by-step explanation:
[tex]\bigg (-1\dfrac{1}{2} \bigg) \cdot \dfrac{2}{3} =-\dfrac{3}{2} \cdot \dfrac{2}{3} =-1[/tex]
Al sumar 2x+5y-4z+9 y 2x-4y+6 se obtiene?
Answer: (Responder)
4x + y + 15 – 4z
Step-by-step explanation: (Explicación paso a paso)
(2x + 5y – 4z) + (9 + 2x – 4y + 6)
Group Like Terms (Agrupar términos similares)
2x + 2x + 5y – 4y – 4z + 9 + 6
Add Similar Elements (Agregar elementos similares)
4x + 5y – 4y – 4z + 9 + 6
4x + y – 4z + 9 + 6
Add The Numbers (Suma los números)
4x + y + 15 – 4z
A table contain 30 milligrams of medications. How many tablets will be needed to provide with 240 milligrams of medication
Answer:
8 tablets
Step-by-step explanation:
Answer:
8 tablets
Step-by-step explanation:
240/30
40% of
a number is 8 more than the
number
Which is the number
Choose the graph of the linear equation 24x + 64y = 384!
?
pls answer fast
Answer: A the first one
Akili has two tests next week. The probability that he will pass the first test, science, is 3 4 . How he does on that test affects how he will do on his math test. If he passes science, then the probability that he will also pass the math test is 4 5 ; otherwise, the probability is only 1 3 that he will pass the math test. What is the probability he passes exactly one test
Answer:
0.2333 = 23.33% probability he passes exactly one test
Step-by-step explanation:
We have these following probabilities:
3/4 probability that he passes the first test.
If he passes the first test, 4/5 probability that he passes the math test.
If he does not pass the first test, 1/3 probability that he passes the math test.
What is the probability he passes exactly one test
Two scenarios:
Pass first(3/4 probability) and fails second(1/5 probability).
Fails first(1/4 probability) and passes second(1/3 probability). So
[tex]p = \frac{3}{4}*\frac{1}{5} + \frac{1}{4}*\frac{1}{3} = \frac{3}{20} + \frac{1}{12} = \frac{9 + 5}{60} = \frac{14}{60} = 0.2333[/tex]
0.2333 = 23.33% probability he passes exactly one test
Please help me it’s sixth grade math
Answer:
its and absolute value
1. 5
2. 12.9
please i need help pleasee
I really need help on this one, guys
Answer:
6.2 meters
Step-by-step explanation:
Use pythagorean theorem to find b:
b = √(2.8² - 2.7²) = √0.55 = 0.7 (nearest tenth)
Perimeter of triangle = sum of all its sides = 2.8 + 2.7 + 0.7
Perimeter = 6.2 meters
4) -3x – 2y = -17
9x + 2y = 23
A) (1,7)
B) (10, 7)
C) (5, 7) D) (-7,7)
Answer:
A). (1, 7)
Step-by-step explanation:
-3x – 2y = -17
9x + 2y = 23
____________+
6x = 6
x = 6/6
x = 1
9x + 2y = 23
9(1) + 2y = 23
9 + 2y = 23
2y = 23 - 9
2y = 14
y = 14/2
y = 7
Help plzz best friend if sooooooooooooooooooooooooooooo
Answer:
10
Step-by-step explanation:
Am i right?
Answer:
c.10
Step-by-step explanation:
8/3.2 = 2.5 so times 2.5 by 4 to get 10
P.S. Good luck on edg
Pls help meeeeeee ahhhhhhh!
Answer: 8x+7
Step-by-step explanation:
The first thing you need to do is multiply (x+1) by 7 (this is the part where you use the distributive property). x times 7 is 7x and 1 times 7 is 7. So now you should have x+7x+7. Now just combine like terms. You can add x and 7x but you can't add the one because there is no variable (x) in it. Your final answer should be 8x+7. Hope this helps!
Given that f(x) = 2x and g(x)=2x+5 and h(x)=2x+2 how does g(x) and h(x) compare to f(x)
Answer:
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