Answer:
a) Approximately normal.
b) The mean is 75 years and the standard deviation is 0.8485 years.
c) 0.9909 = 99.09% probability that the mean age exceeds 73 years
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.
Sample of 50 retirees
This means that [tex]n = 50[/tex]
Mean age and standard deviation are 75 and 6 years
This means that [tex]\mu = 75, \sigma = 6[/tex]
a. Describe the shape of the sampling distribution of the sample mean in this case
By the Central Limit Theorem, approximately normal.
b. Find the mean and standard error of the sampling distribution of the sample mean.
By the Central Limit Theorem, the mean is 75 and the standard error is [tex]s = \frac{6}{\sqrt{50}} = 0.8485[/tex]
c. What is the probability that the mean age exceeds 73 years?
This is 1 subtracted by the pvalue of Z when X = 73.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73 - 75}{0.8485}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a pvalue of 0.0091
1 - 0.0091 = 0.9909
0.9909 = 99.09% probability that the mean age exceeds 73 years
Mrs. Stephens bought 3 pounds of tomatoes.How many ounces are equal to 3 pounds?
Answer:
48 ounces
Step-by-step explanation:
16 ounces per pound
3 x 16 = 48 ounces
In a town, 65% of people had high speed internet in their homes. If the population of the town is 80,000, how many
people do not have access to high speed internet in their homes?
Show work
What about the rational equation causes asymptotes?
Answer:Some functions have asymptotes because the denominator equals zero for a particular value of x or because the denominator increases faster than the numerator as x increases.
Step-by-step explanation:
A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 46 cables and apply weights to each of them until they break. The 46 cables have a mean breaking weight of 779 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 99% confidence interval to estimate the mean breaking weight for this type cable.
Answer:
The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 46 - 1 = 45
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 45 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.69
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.69\frac{15.4}{\sqrt{46}} = 6.1[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 779 - 6.1 = 772.9 lb
The upper end of the interval is the sample mean added to M. So it is 779 + 6.1 = 785.1 lb
The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.
please help me for brqinliest im imed
Answer:
77°
Step-by-step explanation:
As we can see ABCD is a cyclic quadrilateral so opposite angles of a cyclic quadrilateral is supplementary.
< A + <B = 180° { being opposite angles of cyclic quadrilateral }
2x + 9° + 3x + 1° = 180°
5x + 10° = 180°
5x = 180° - 10°
5x = 170°
x = 170° / 5
x = 34°
Now
< A = 2x + 9°
= 2 * 34° + 9°
= 77°
Hope it will help :)❤
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level. What would be the appropriate alternative hypothesis if he wanted to substantiate his suspicion
Answer:
The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]
Step-by-step explanation:
At the null hypothesis, we test that the mean is equal to a certain value.
At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 238[/tex]
A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu > 238[/tex]
A carpenter needs to cut a 3.9 meter long piece of wood into 3 equal lengths. How long should each piece be in millimeters?
Answer:
1300
Step-by-step explanation:
Answer:
1300
Step-by-step explanation:
8. Misty created the number pattern below. 32, 28, 24, 20, ... If n represents a number in this pattern, which rule could be used to find the next number in the pattern?
Answer:
An = 32 - (4*(n-1))
Step-by-step explanation:
the starting term for this pattern is 32 (which you will need to include in the "rule")
you also know that the next term is the previous term - 4
so!
we can write this pattern as
An = 32 - (4*(n-1))
An = any number of term in the pattern
- ex). A2 = 28, A3 = 24, etc
n = the nth term
- the 3rd term = 24, the fourth term = 20, etc
I need help please.
Answer:
B
Step-by-step explanation:
Put "Volume of a Cone" in your browser and all you have to do is type the height and radius.
a soccer game started at 2:15p.m. and ended at 3:35p.m. how long did the game last
Please help!!!!!!!!!!
Answer:
104 ft^2
Step-by-step explanation:
Before we start, one thing to notice is the 90 degrees symbol at the corners. This lets you know a rectangle has four 90 degrees angle, which will help in the next step.
First, separate the shape to become three rectangles.
After you've done that, start with the first recantgle on the left.
The edges are 8 and 5. To find the area, you must multiple 8 by 5.
8 * 5 =40
The area is 40 for the first rectangle.
Next, we do the second rectangle to the right of the first one.
oThe edges are 6 and 4. We know it is four because the full length on the rectangle on the left is 8 and below the 6 ft is the place that says 4 ft. The 6ft line cuts to rectangle in half so the other edge will be 4 ft. (Hope that made sense )
Now we find the area of the second rectangle by multiplying 6 and 4
6 *4 = 24
Now we conclude with the third rectangle. We know one edge which is 5 and the other edge will be 8 because, at the opposite end, it tells us the length is 8.
Now we multiply 8 and 5.
8 * 5 = 40.
Now, the three numbers we have found are 40, 24, and 40. Our final step is to add up these three numbers from the rectangles we made to find the area.
40 + 24 + 40 = 104
The area will be 104 ft^2
I hope this explanation helped and have a good day!
solving and graphing inequalities
Answer:
wssp i can help
Step-by-step explanation:
An elementary school held a fundraiser. Students sold candles and plants. The plants sold for $12.50 each and the
candles sold for $3.75 each. The school raised $3,987.50 and sold 410 candles and plants altogether. How many
CANDLES did they sell?
Answer:
The school sold 130 candles
Step-by-step explanation:
Given that the plants sold for $12.50 each and the candles sold for $3.75 each. If the school raised raised $3,987.50 and sold 410 candles and plants altogether then the number of candles and plants sold may be computed simultaneously as follows:
Let the number of candles sold be c and the number of plants sold be p. If the school sold 410 candles and plants altogether
p + c = 410
p = 410 - c
if the plants sold for $12.50 each and the candles sold for $3.75 each and the school raised raised $3,987.50
12.5p + 3.75c = 3,987.50
12.5(410 - c) + 3.75c = 3,987.50
5125 -12.5c +3.75c = 3,987.50
-8.75c = 3,987.50 - 5125
-8.75c = -1137.5
c = -1137.5/-8.75
= 130
The figure below is formed from a triangle and a
square. The square has sides that measure 5 units.
Find perimeter of the entire figure.
classify the triangle base on angles and sides
Answer:
C. Acute; isosceles
Step-by-step explanation:
As you can see 2 sides of the triangle are equal to 10 which means they are congruent. It's an isosceles triangle because it has two congruent sides.
You can also see that none of the angles form 90 degrees or more which means they are acute angles.
Hope that helps
Help math eh at t were rhehh
It takes 8 blocks with side lengths of 4 meter to fill a rectangular prism.
The rectangular prism has a volume of
cubic meter.
1/8
Reset
1/4
1/2
1
Me das mas información?
Answer:
1
Step-by-step explanation:
help for 10 points plsssss
Answer:
on math way you can take a picture of your problem. hope those helps
Step-by-step explanation:
Which math term is it for this one ?
Answer:
option D
the set of all points that are a fixed distance from a given point
hope it helps
A triangular fence is built with sides each of length 15 m, 14 m, and 24 m, respectively. To the
nearest degree, what is the measure of the smallest angle made by the fence?
9514 1404 393
Answer:
33°
Step-by-step explanation:
The law of cosines tells you ...
a² = b² +c² -2bc·cos(A)
Solving for A, we get ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((15² +24² -14²)/(2·15·24)) = arccos(605/720)
A ≈ 32.8305°
The smallest angle is about 33°.
Which equation is equivalent to 3-4x=12
We have a linear equation here.
3 - 4x = 12
Subtract 3 from both sides.
3 - 3 - 4x = 12 - 3
-4x = 9
Divide both sides by -4 to find x.
-4x/-4 = 9/-4
x = -9/4
The value of solution of expression is,
⇒ x = - 9 / 14
WE have to given that;
A mathematical expression is,
⇒ 3 - 4x = 12
Now, WE can simplify as;
⇒ 3 - 4x = 12
Add 4x both side,
⇒ 3 - 4x + 4x = 12 + 4x
⇒ 3 = 12 + 4x
Subtract 12 both side, we get;
⇒ 3 - 12 = 14x
⇒ - 9 = 14x
⇒ x = - 9 / 14
Thus, The value of solution of expression is,
⇒ x = - 9 / 14
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Hey guys can you guys help me thanks :)
Answer:
d
Step-by-step explanation:
60x9 =540
HELP WILL GIBE BRAINLIEST.
HOW MUCH IS IT FOR 1
Answer:
small is 0.018
medium is 0.016
large is 0.010
The school debate team sold candy bars as fundraiser. The earnings are graphed below. What is the rate the debate team charged for each candy bar ?
Answer:
were is the graph lol
Helpppppppppp fasttttttttttttttttttt
Answer:
first 2 , second 50, third 8
Step-by-step explanation:
Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if if the sample mean weight is significantly different than 68g. She takes a random sample of 100 eggs and finds a mean weight of 67g and a sample standard deviation of 1g.
Required:
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?
Answer:
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Step-by-step explanation:
To solve this question, we use 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 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.
Mean weight of 67g and a sample standard deviation of 1g.
This means that [tex]\mu = 67, \sigma = 1[/tex]
Sample of 4
This means that [tex]n = 4, s = \frac{1}{\sqrt{4}} = 0.5[/tex]
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?
This is the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 67}{0.5}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Answer:
-10
Step-by-step explanation:
Khan
really need help! anything would be appreciated
A dot plot titled Number of runs scored going from 0 to 5. 0 has 2 dots, 1 has 4 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot. What is a dot plot and how do you read it? Check all that apply. A dot plot displays data values as dots above a number line. Dot plots show the frequency with which a specific item appears in a data set. There was 1 run in 5 of the games. There were 0 runs in 2 of the games. Dot plots show the distribution of the data. There were a total of 19 games.
Answer:
abdef (those are the answers)
Step-by-step explanation:
Answer:
all but C
Step-by-step explanation:
HELP ME WITH A MATH PROBKEM Type a number that has a value less than 4.7|
Answer:
i think
all the numbers between
0 to 4.6
How do I start this problem? I don't need help with the graphing part.
Answer:
x = 6 , y = 0 (x , y) = (6 , 0)
x = 12, y = 3 (x , y) = (12 , 3)
x = 24, y = 9 (x , y) = (24 , 9)
Step-by-step explanation:
Simply plug in a x, and find a y that would make the equation true:
When x = 6:
6 - 2y = 6
6 (-6) - 2y = 6 (-6)
-2y = 0
(-2y)/-2 = (0)/-2
y = 0
When x = 6, y = 0 (x , y) = (6 , 0)
When x = 12:
12 - 2y = 6
12 (-12) -2y = 6 (-12)
-2y = -6
(-2y)/-2 = (-6)/-2
y = 3
When x = 12, y = 3 (x , y) = (12 , 3)
When x = 24:
24 - 2y = 6
24 (-24) - 2y = 6 (-24)
-2y = -18
(-2y)/-2 = (-18)/-2
y = 9
When x = 24, y = 9 (x , y) = (24 , 9)
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