Answer:
a. 0.1038 = 10.38% probability that the sample mean is more than 59 pounds.
b. 0.6772 = 67.72% probability that the sample mean is more than 56 pounds.
c. 0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.
d. 0.0146 = 1.46% probability that the sample mean is less than 53 pounds.
e. 0% probability that the sample mean is less than 49 pounds.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, 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.
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. The population standard deviation of annual usage is 12.3 pounds.
This means that [tex]\mu = 56.8, \sigma = 12.3[/tex]
Sample of 50:
This means that [tex]n = 50, s = \frac{12.3}{\sqrt{50}} = 1.74[/tex]
a. More than 59 pounds
This is 1 subtracted by the pvalue of Z when X = 59.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 56.8}{1.74}[/tex]
[tex]Z = 1.26[/tex]
[tex]Z = 1.26[/tex] has a pvalue of 0.8962
1 - 0.8962 = 0.1038
0.1038 = 10.38% probability that the sample mean is more than 59 pounds.
b. More than 56 pounds
This is 1 subtracted by the pvalue of Z when X = 56. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228
1 - 0.3228 = 0.6772
0.6772 = 67.72% probability that the sample mean is more than 56 pounds.
c. Between 56 and 57 pounds
This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56.
X = 57
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{57 - 56.8}{1.74}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a pvalue of 0.5438
X = 56
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228
0.5438 - 0.3228 = 0.2210
0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.
d. Less than 53 pounds
This is the pvalue of Z when X = 53.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{53 - 56.8}{1.74}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
0.0146 = 1.46% probability that the sample mean is less than 53 pounds.
e. Less than 49 pounds
This is the pvalue of Z when X = 49.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49 - 56.8}{1.74}[/tex]
[tex]Z = -4.48[/tex]
[tex]Z = -4.48[/tex] has a pvalue of 0
0% probability that the sample mean is less than 49 pounds.
Can somebody please give me the answer I will mark u brilliant
Answer:
x = 6.7
Step-by-step explanation:
We know that 3.5 + x = 10.2, so if we do inverse operations we can find out the value of x.
10.2 - 3.5 = 6.7
we can check our work by substituing it back in the equation for x
6.7 + 3.5 = 10.2
so now we know that x = 6.7. I hope this helps :)
Answer: x=6.7
Step-by-step explanation:
x+3.5=10.2
-3.5 -3.5
x= 6.7
4+4????????/??????//?? PLEASESESERK ALKSDJFKLASDF ASLKDJ FAJSDFJASDJF AJSDF
Answer:
8
Step-by-step explanation:
❤❤❤❤❤❤❤❤❤❤❤❤❤
Have a great day ❤
Answer:
8
Step-by-step explanation:
YOU'REWELCOMEADFHTGHEFGREEWJUIFGYREHFBNCNBASDFHJLKJHGFDS
10
Gary, Nancy, and Jamal are trying to write an inequality where all values in the set of numbers below make the inequality true.
{0, 1, 3, 4, 6, 12}
Consider their inequalities.
Gary: 6 > 0.50
Nancy: 30 -t < 18
Jamal: 12
Which student(s) wrote an inequality that is true for all values in the set of numbers? Select your answer from the drop-down list
Only Gary as the
Only Gary
Only Nancy
Only Jamal
Only Gary and
Nancy
Only Gary and
Jamal
Only Nancy and
Jamal
Answer:
Jamal's inequality is correct
Step-by-step explanation:
Given
[tex]Sets:\{0,1,3,4,6,12\}[/tex]
Gary: [tex]6>0.5t[/tex]
Nancy: [tex]30 -t \le 18[/tex]
Jamal: [tex]12 \le t+12[/tex]
Required
Which of the inequalities is/are true
Gary: [tex]6>0.5t[/tex]
[tex]6>0.5t[/tex]
Divide both sides by 0.5
[tex]\frac{6}{0.5} > \frac{0.5t}{0.5}[/tex]
[tex]12 > t[/tex]
Rewrite as:
[tex]t < 12[/tex]
Gary's inequality is false because: [tex]12 = 12[/tex]
Nancy: [tex]30 -t \le 18[/tex]
[tex]30 -t \le 18[/tex]
Collect like terms
[tex]-t \le 18 - 30[/tex]
[tex]-t \le -12[/tex]
Divide both sides by -1
[tex]t \ge 12[/tex]
Nancy's inequality is incorrect because: 0,1,3,4 and 6 are less than 12
Jamal: [tex]12 \le t+12[/tex]
[tex]12 \le t+12[/tex]
[tex]12 - 12 \le t[/tex]
[tex]0 \le t[/tex]
Rewrite as:
[tex]t \ge 0[/tex]
Jamal's inequality is correct because: 0,1,3,4,6 and 12 [tex]\ge 0[/tex]
What geometric
constructions can have a
perpendicular bisector?
Answer:
A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.
I need help. correct answer gets brainliest
Answer:
can you zoom in on it
Step-by-step explanation:
Given below are descriptions of two lines.
Line 1: Goes through
(
−
5
,
−
9
)
and
(
12
,
42
)
Line 2: Goes through
(
−
9
,
6
)
and
(
−
3
,
4
)
The slope of Line 1 is
m
=
The slope of Line 2 is
m
=
Finally, which of the following is true?
Line 1 is parallel to Line 2.
Line 1 is perpendicular to Line 2
Line 1 is neither parallel nor perpendicular to Line 2
Answer:
Yes
Step-by-step explanation:
Five plumbers charge different hourly
rates: $35, $42, $52, $38, and $42.
Find the mean, median, mode, MAD,
and IQR of these values. Which
measure of center and which measure
of variability best describe the data?
Jordan was planting a garden. She wanted the bottom of the garden to have an area of 48 feet. She wanted the width to be 3/4 the length. What are the dimensions of the garden
what's nine times 4?
Answer:
9 x 4 = 36
9 multiply by 4 is 36.
Answer:
36
Step-by-step explanation:
If you do 9 * 9 * 9 * 9 you would get 36.
Hence, study your nines. (lol)
Hope this helps! ;)
What is the simplified form of the following expression? 4x2|y3z| 4x4y8
Answer:
16x⁶y⁸|y³z|.........
Answer:
B
Step-by-step explanation:
EDGE
Write a proof for the statement If a quadrilateral is a square, then the quadrilateral is a rectangle
Answer:
this is because a quadrilateral is a four sided polygon.
and this means square and rectangle are quadrilaterals.
You are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this observation, you conclude that there is a _______ between the temperature and hot beverage sales at this coffee shop. Group of answer choices negative relationship curvilinear relationship no relationship positive relationship
Answer:
negative relationship.
Step-by-step explanation:
An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).
This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.
Cause and effect can be defined as the relationship between two things or events in which an occurrence one (cause) leads to the occurrence of another (effect).
A negative relationship or correlation can be defined as the relationship between two variables in which there exist an inverse relationship between them i.e as one variable increases, the other decreases and vice-versa.
In this scenario, you are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this observation, you conclude that there is a negative relationship between the temperature and hot beverage sales at this coffee shop because for the temperature to get colder it would decrease and for the hot beverages to be hot, its temperature must be increased.
A 4-foot-long sandwich is cut into servings that are each ; foot long. How many servings will there be after the sandwich is cut?
Answer:
$ because there are 4ft cut into one foot each equals 4
Step-by-step explanation:
I will give out 40 points for the four answers but if you just take the points and don't answer properly I will report you
Answer:
A:-3<x<13
B:-3=<x=<13
C:-3=<x<13
D:-3<x=<13
Step-by-step explanation:
Ok, first lets do A
-3 and -13 and the endpoints and the dots are hollow so its not including
therefore the answer is -3<x<13
next, B
same endpoint this time but both dots are filled in so they are included
therefore: -3=<x=<13
(I'm typing on a keyboard!!! i can't do the fancy symbols lol)
C
same endpoints again but -3 is black and 13 is not
so: -3=<x<13
D
I think you have got the hang of it now probaly
-3 is not filled and 13 is
answer is -3<x=<13
Hope this helps :)
Pleaseeeeeeeeee help
Answer:
80 in2
Step-by-step explanation:
10x8=80
A= 80 in2
Answer:
For base area? Its 80 in².
Which is equivalent to P(z ≥ 1.4)?
Answer:
1-P(z<1.4)
Step-by-step explanation:
Trust me the answer is 1-P(z<1.4).
BTW the thing between 1 and P is a minus sign
Answer:
B. 1-P(z<1.4)
8%
B. 26%
Step-by-step explanation:
Solve the exponential equation.
(½)x = 32
-5
1/5
-1/5
Answer:
-5
Step-by-step explanation:
(1/2)^x=2^-x
32=2^5
2^-x=2^5
-x=5
x=-5
Answer:Answer:
-5
Step-by-step explanation:
(1/2)^x=2^-x
32=2^5
2^-x=2^5
-x=5
x=-5
Step-by-step explanation:
To draw a line that is parallel to 9x+12y=16, what should the slope of the line be?(1 point)
A. 4/3
B. -3/4
C. -4/3
D. 3/4
Answer:
Hi how are you doing today Jasmine
In ΔMNO, the measure of ∠O=90°, the measure of ∠M=46°, and NO = 96 feet. Find the length of OM to the nearest tenth of a foot.
Answer:
92.7 ft
Step-by-step explanation:
A fair spinner has 10 equal sections: 4 red, 3 blue and 3 green.
It is spun twice.
What is the probability of getting the same colour twice?
Answer:
4 divided by 10 is 40% 3 divided by 10 is 30 percent
Step-by-step explanation:
for red there would be 40 percent probability and green and blue both have 30% probability.
The first term of an arithmetic sequence is 3. The common difference of the sequence is 1.5 tune the first term. Write the next five terms in the sequence:
Answer:
3, 7.5, 12, 16.5
Step-by-step explanation:
Tn = a + (n-1)d
a = 3 and d = 1.5×3 = 4.5
T2 = a + d = 3 + 4.5 = 7.5
T3 = a + 2d = 3 + 2(4.5) = 12
T4 = a + 3d = 3 + 3(4.5) = 16.5
Hope its correct and have a great day :)
1. Is a Square a rectangle?(Always, Never, Sometimes. Are all the answers you can say for these)
2. is a trapezoid a parallelogram?
3. does Quadrilaterals
have for congruent sides?
4. is a parallelogram a rectangle?
Answer:
1. sometimes
2. always
3. always
4. always
Step-by-step explanation:
Declan's goal is to score 90% on the upcoming science test. If there are 50 questions on the test, how many does he need to answer correctly?
Answer:
45
Step-by-step explanation:
Find the average rate of change of f(x)=x^2-4x+1 from x=3 to x=7 .
Answer:
7
Step-by-step explanation:
Use the Distributive Property to
REWRITE -3(c-8)
Answer:-3c +24
Step-by-step explanation:
-3(c) and -3 (-8)
-3c and two negatives equal a positive, so +24
Does anyone know????????
Answer:
1) -3/2
Step-by-step explanation:
The common ratio is the amount you multiply by to get to the next number in the sequence. To calculate this you will need to divide the term by its preceding term.
For example (3/4) / (-1/2)
When dividing by fractions you should apply KCF (Keep Change Flip), so you will end up with (3/4) x (-2/1) = -3/2
Check this by doing the next term (-9/8) / (3/4)
When dividing by fractions you should apply KCF (Keep Change Flip), so you will end up with (-9/8) x (4/3) = -3/2
The table shows the amount in fluid ounces of
each ingredient Randolph used to make fruit
punch for a party.
How many pints of this fruit punch did Randolph
make?
Fruit Punch
1,792 pints
Ingredient
Amount Used
(fluid ounces)
B 102 pints
Orange juice
24
7 pints
Apple juice
24
Lime soda
64
D 14 pints
Answer:
Step-by-step explanation:
Please help with this math question'
Answer:
The rocket's maximum height will be 1424 feet.
It will reach that height in 4 seconds.
It will reach the ground in 8 seconds.
Step-by-step explanation:
One easy way to find the peak is to find the derivative and solve for zero:
h(t) = -16t² + 128t + 1680
To find the derivative of each term in that format, you simply multiply the coefficient by the exponent, and reduce the exponent by one. In the case of terms with no variable, they disappear. That gives us:
h'(t) = -32t + 128
This derivative describes the rate of change of h with respect to t, so to find the peak, we simply need to solve it for zero:
0 = -32t + 128
32t = 128
t = 4
So the maximum height occurs when t = 4. Let's plug it in to the original equation:
h(t) = -16t² + 128t + 1680
h(4) = -256 + 512 + 1680
h(4) = 1424
So the rocket's maxiumum height is 1424 feet.
And we've already answered the second question, it happens at 4 seconds.
Also, the amount of time going up will be the same as the amount of time going down, which means that it will reach the ground in twice that time, or 8 seconds.
(2+5x)9= combine like terms
Answer:
18+45x
Step-by-step explanation:
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.6 feet and a height of 3.4 feet. Use percentage to compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round your final answer to the nearest tenth.
(I will mark the person who gets the answer correct as brainliest)
Answer:
89.7 is the percent
Step-by-step explanation:
38.41/43.7=0.879 (87.9%).