Answer:
a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large.
Step-by-step explanation:
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.
So, according to the above text, the correct answer is given by option a, that is, if the sample is large, the sampling distribution of the sample mean will be approximately normal, that is, trend towards a normal distribution.
Can someone give me the answer and explain it to me? Pls, I’ll mark brainiest.
An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis that there is no difference between the average yields using the different fertilizers, if the test statistic is 1.53 and the critical value is 2.57 then what is your conclusion concerning the null hypothesis?
Answer:
We do not reject the null
Step-by-step explanation:
Given that :
Sample size, n = 41
Test statistic ; Zstatistic ;= 1.53
Critical value ; Zcritical ; = 2.57
The null hypothesis H0 ;
H0: μ1 - μ2 = 0
Alternative hypothesis, H1 ;
H1: μ1 ≠ μ2
Decision region :
Reject Null ; if |Zstatistic ≥ Zcritical|
Zstatistic > Zcritical
Result :
1.53 < 2.57
Zstatistic < Zcritical
Hence, we do not reject the null ; there is no significant evidence that there is difference in the average yield of the two samples.
Suppose that a standardized biology exam has a mean score of 80% correct, with a standard deviation of 3. The school administration believes that the new class of freshmen have a different mean exam score. A sample of 65 students from the freshmen class is used and a mean score of 76% correct is obtained.
Calculate a 99% confidence interval. List the lower bound (rounded to 2 decimal places) and the upper bound (rounded to 2 decimal places).
Answer:
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
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].
A sample of 65 students from the freshmen class is used and a mean score of 76% correct is obtained.
This means that [tex]n = 65, \pi = 0.76[/tex]
99% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 - 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.6236[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 + 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.8964[/tex]
0.6236*100 = 62.36%
0.8964*100 = 89.64%
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
Simplify (-9p+7)-(-9p+3)
[tex]\tt{}( - 9p + 7) - (9p + 3)[/tex]
[tex]\tt{} - 9p - 7 + 9p + 3[/tex]
[tex]\tt{}7 - 3[/tex]
[tex]\tt{}4[/tex]
the length of a pool 2 km long is represented on a map with a length of 20cm. what is the map scale used?
Answer:
The scale used is 1: 10,000 cm.
Step-by-step explanation:
Given that the length of a pool 2 km long is represented on a map with a length of 20cm, to determine what is the map scale used the following calculation must be performed:
2 km = 2,000 m
1m = 100cm
2,000 x 100 = 200,000
20: 200,000
10: 100,000
1: 10,000
Thus, the scale used is 1: 10,000 cm.
Answer:
10,000
Step-by-step explanation:
FOR THE SMART MATH PEOPLE
WILL GIVE BRAINLIEST
This figure shown is NOT a square because a square has all angles are 90º.
It is a rhombus and a parallelogram because they both have a parallel sides(At least 2). NOW GIVE ME BRAINLIEST!!!!
Find the area of each of the following
Answer:
The area of this shape is 252.
Step-by-step explanation:
Cut the right piece of the shape into a triangle of 90 degrees, which makes the shape divided into 2 triangles and 1 rectangle.
9 x 13 = 117 (rectangle part)
15 x 9 = 135, 135/2 = 67.5
15 x 9 = 135, 135/2 = 67.5
67.5 + 67.5 + 117 = 252
DUE soon! For an unknown parent function f(x), write a function g(x) that is:
vertically stretched by a factor of 2,
shifted up 5 units, and
shifted right 4 units.
Explain how your function accomplishes these transformations.
See I don't know if you can choose whichever parent function to start off.
Answer and Step-by-step explanation:
The parent function is just f(x) = x.
See, the transformations equation of a parent function is as follows:
f(x) = a(x - h) + k
Where:
a is the scaling factor,
h is the horizontal (left and right) changing factor, and
k is the vertical (up and down) changing factor.
So, now we apply the transformations to this parent function by writing it in function g(x).
Vertically stretch by factor of 2: g(x) = 2x
Shifted up 5 units: g(x) = 2x + 5
Shifted left 4 units: g(x) = 2(x - 4) + 5
g(x) = 2(x - 4) + 5 is the function.
This function accomplishes these transformation by having 2 be the scale factor, 4 be the horizontal shift, and 5 be the the vertical shift.
#teamtrees #PAW (Plant And Water)
Find the slope of the line that goes through the
(-4,6) and (2.1)
Answer:
-5/6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-6)/(2-(-4))
m=-5/(2+4)
m=-5/6
Which of the following is equivalent to
X^2 - 8x - 7 =0
A.) (x-8)^2 = 15
B.) (x-4)^2 = 15
C.) (x-8)^2 = 23
D.) (x-4)^2 = 23
Answer: it will be D
Step-by-step explanation: if You graph them you will get the same coordinate plates
This graph represents a linear function.
Enter an equation in the form y=mx+b that represents the function
described by the graph.
*Note: Uses only numbers and symbols, no spaces. If there is a fraction,
10
1
make it improper and use parentheses (ie. y =
72+ z will be typed
as y=(10/7)x+(1/2)]
Type your answer
Answer:
y=1x-3
Step-by-step explanation:
In ΔQRS, the measure of ∠S=90°, the measure of ∠R=53°, and SQ = 93 feet. Find the length of RS to the nearest tenth of a foot.
Answer 70.1
Step-by-step explanation:
HELP ASAP ILL GIVE BRAINLIEST
Write an expression for
The product of eleven times a number less than 12
11(n - 12)
12n - 11
11n - 12
12 - 11n
Answer:
11n - 12
Step-by-step explanation:
The answers for the March 22 Recording Check
1. Solve the following one-step equation.
x+5=−7
x = -12 This is the correct answer
x = 2
2. An expression does NOT have an equal sign
The answer would be True
2.4 x 6.7 =
I need the work too
Answer:
16.08
Step-by-step explanation:
Problem 5.A miner is trapped inside a mine and has access to 3 doors. The first door leads to a tunneland can take him to safety in 3 hours. The second door is a trap and brings him back to the mine againafter 5 hours through a tunnel. The third door also is a trap that brings him back to the mine after 7 hoursthrough a tunnel. The miner at all times is equally like to choose any of the doors. (In the darkness he canhardly distinguish the three). What is the expected length of time until he reaches safety
Answer:
Expected time is 15 hours for him to get to safety.
Step-by-step explanation:
We define X as the time that this miner would get to safety.
We define Y as the door he chooses initially.
P(Y= 1) = P(Y=2)=P(Y=3) = 1/3
We have E[X|Y=1] = 3
E[X|Y] = 5 hours + E[X}
E[X|Y] = 7 hours + E[X]
Then we have
E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])
We cross multiply
3*E[X] = (15 + 2E[x])
3E[X] - 2E[X] = 15
E[X] = 15
So the time it would take to get him to safety is 15 hours
In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 17% have inadequate calcium intake. For those who are 11 to 13 years of age, 54% have inadequate calcium intake. Use Bayes's rule to find the probability that a child from this population who has inadequate intake is 11 to 13 years old.
Answer:
0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Inadequate intake
Event B: Is 11 to 13 years old.
48% are 11 to 13 years of age.
This means that [tex]P(B) = 0.48[/tex]
For those who are 11 to 13 years of age, 54% have inadequate calcium intake.
This means that [tex]P(A|B) = 0.54[/tex]
Probability of inadequate calcium intake:
0.17 of 0.52(5 to 10 years old)
0.54 of 0.48(11 to 13 years old). So
[tex]P(A) = 0.17*0.52 + 0.54*0.48 = 0.3476[/tex]
Find the probability that a child from this population who has inadequate intake is 11 to 13 years old.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.48*0.54}{0.3476} = 0.7457[/tex]
0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.
Which graph shows the line y = 4x - 2?
Answer:
Line A
Step-by-step explanation:
Line A is the blue line with the y-intercept of (0,-2) and positive slope of 4.
⚠️HELP DUE TODAY⚠️
The area of a rectangular garden is x^2- 5x - 24. Factor the trinomial to find the dimensions of the rectangular garden in terms of x
Answer: (why is it 5 points?) Thats ok.
5 times what X is - 24 meaning whatever X is also by sry i don't make a lot of sense but i'm smart and know the answer. I will change it later after i find out which shouldn't take too long.
Step-by-step explanation:
Thanks, stay safe, have a great life! Byes! Brainliest then i will give answer! ;) :) :P XD :3 (: hehe :)
this question is confusing me
2/5 x 10/22 in simplest form
Answer:
2/11
Step-by-step explanation:
You would have to do 2 times 10 which equals 20. Than 5 times 22 which is 110. No to reduce you have to find the Greatest Common faction which is 10. So 20 divided by 10 equals 2 and 110 divided by 10 is 11.
How many 0.5 ribbons will be cut from a 8 meter
Answer:
16 ribbons
Step-by-step explanation:
Given
[tex]Length = 8\ meter[/tex]
[tex]Ribbon\ Length = 0.5\ meter[/tex]
Required
Determine the number of ribbons
This is calculated as:
[tex]n = \frac{Length}{Ribbon\ Length}[/tex]
[tex]n = \frac{8m}{0.5m}[/tex]
[tex]n = \frac{8}{0.5}[/tex]
[tex]n = 16[/tex]
Describe the zeros of the graphed function.
A.
The function has three distinct real zeros.
B.
The function has two distinct real zeros and two complex zeros.
C.
The function has four distinct real zeros.
D.
The function has one distinct real zero and two complex zeros.
Answer:
A
Step-by-step explanation:
it intersects x axis at three points.
if my answer helps please mark as brainliest.
I did part a and b, i need help with the question that says " does the cup hold the exact volume of scoop of ice cream" and part C
Answer:
See below.
Step-by-step explanation:
Part a is correct.
The volume of part b is correct.
The volume of a scoop is 268 cm^3.
The volume of the cylindrical cup is 402 cm^3.
Part b)
Question: Does the cup hold the exact volume of the scoop? Explain.
Answer: No. The cup holds 402 cm^3 up to the brim. If you overfill it like the picture shows, it will hold even more than 402 cm^2. A scoop is only 268 cm^3, so a cup holds more than the scoop.
Part c)
volume of cone = (1/3)(pi)r^2h
V = (1/3)(3.14159)(4 cm)^2(8 cm)
V = 134 cm^3
ASAP HW HELP
if you don’t know answer don’t even comment
Answer:
y=1/4x-3
Step-by-step explanation:
Fifty people put there name
into a two different drawings
(30 males and 20 females).
One drawing is for an iPad and
the other is for a flat screen
TV. What is the probability
that a female will win the iPad
and a male win the flat
screen?
7.SP.8
Solve 3(4x + 5) = 33
You may use the flowchart to help you if you wish.
Answer:
This is so simple omg
Expand ”4x+5” out so...
12x + 15 = 33
12x = 33 - 15 = 18
12x = 18
x = 1.5
Answer:
Step-by-step explanation:
In a group of 84 kids, three-sevenths bought their lunches. Of those who bought their lunches, 9 got a slice of pizza. What is the fraction of the students who bought their lunches got a slice of pizza. Write your fraction in simplest form.
3/7x84=36
Ans: 9/36=1/4
Find the length of DC.
Answer:
sqart(89) in
Step-by-step explanation:
As triangle ABC is a right triangle, so sqrt(5^2 + 8^2) = sqrt(89) approximately 9.43 in.
Two angles are supplementary. One angle measures (3x+8) and the other measures (6x+64) what is the value of X?
this is my last question
Answer: B
Step-by-step explanation:because my teacher said she having trouble