Answer:
0.0062 = 0.62% probability that the sample mean is less than $650.
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.
Mean of $675 and a standard deviation of $80.
This means that [tex]\mu = 675, \sigma = 80[/tex]
A random sample of 64 families in this city paying for childcare is selected.
This means that [tex]n = 64, s = \frac{80}{\sqrt{64}} = 10[/tex]
Find the probability that the sample mean is less than $650.
This is the pvalue of Z when X = 650.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{650 - 675}{10}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
0.0062 = 0.62% probability that the sample mean is less than $650.
The probability that the sample mean is less than $650 is 0.62%.
The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\sigma=standard\ deviation,\mu=mean,n=sample\ size\\\\\\Given \ \mu=675,\sigma=80,n=84, hence:\\\\For\ x<650:\\\\z=\frac{650-675}{80/\sqrt{64} } =-2.5[/tex]
From the normal distribution table:
P(x < 650) = P(z < -2.5) = 0.0062 = 0.62%
The probability that the sample mean is less than $650 is 0.62%.
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Help rn ahhhh please
Answer:
117π or 367.56634047
Step-by-step explanation:
Volume = π × r² × h (r=radius and h=height)
Volume = π × 4² × 13
Volume = π × 9 × 13
Volume = π × 117
Volume = 117π
15 less than 3 times a number is 5 more than half of the number.
Answer:
Mystery Number is 8
Step-by-step explanation:
3x - 15 = 5 + 1/2x
3x - 1/2x = 15 + 5
5/2x = 20
x = 20 / 5/2
x = 20 * 2/5
x = 40 / 5
x = 8
HELP PLEASE BRAINLYIST
Examine the diagram. It is not drawn to scale.
Wh at is the m angle 3?
Х
m angle 3=
Answer:
isn't it just 50°
Step-by-step explanation:
180=a straight line.
you are given 75° and 55°
75+55=130
180-130
Answer:
105
Step-by-step explanation:
Chupapi
Some loser deleted my answers
That's why it says 1 answer and 1.5k people helped
The diameter of a circle is 3 meters. What is the circumference?
Answer:
C≈9.42m
Using any of this formulas
C=2πr
C=2πrd=2r
Solution:
C=πd=π·3≈9.42478m
Noah has $5.
1.
a.
Elena has 40% as much as Noah. How much does Elena have?
b.
Compare Elena's and Noah's money using fractions. Draw a diagram to
illustrate.
Answer:
a. $4
b. Noah has 5/5. Elena has 4/5.
Step-by-step explanation:
Noah has $5.
a.
Elena has 80% of Noah's money.
80% of $5 = 0.80 * $5 = $4
b.
Noah has $5. We can consider $5 to be the full amount.
A full amount is 100% or 1 or 5/5.
Elena has 80% of Noah's money, so she has 80/100 of Noah's money.
80/100 reduces to 4/5.
Noah has 5/5, and Elena has 4/5.
The money that Elena has is $2.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The given problem can be solved as follows,
(a) The amount of money Elena has is 40% of that of Noah.
It can be written as follows,
40% × 5
= 40/100 × 5
= 2
(b) Since the Elena has 40% of the Noah's money,
In the form of fraction it can be written as follows,
40% = 40/100
= 2/5
This can be represented in a diagram as follows,
In the diagram shown the circle has in total 5 sectors of which 2 yellow sectors represent Elena's money.
Hence, the amount of money Elena has is $2 which is shown in the diagram.
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Please answer the questions attached below
Answer:
Step-by-step explanation:
The parallelogram is two congruent triangles. Area of blue triangle is ½·2·2 = 2 units²
Area of parallelogram = 4 units²
:::::
area of blue parallelogram = 4×9 = 36 units²
:::::
area of green parallelogram = 3×5 = 15 units²
An expression is shown.
95-34
What is the value of the expression?
Answer:
61
Step-by-step explanation:
95
- 34
_______
61
Help... need it right now ;-;
Answer:
1
Step-by-step explanation:
|3 + 2 - 6| = |5 - 6| = |-1| = 1
Answer:
1
Step-by-step explanation:
Hello There!
For this one, like the other one, all we have to do is plug in the values
so
l 3 - (-2) + (-6) l
3 - (-2)
the two negative signs cancels out so now its
3+2 which is equal to 5
5-6=-1
l-1l remember l l means absolute value and the absolute value of -1 is 1 so the answer is 1
Tara and Mallory are practicing their passing at a volleyball practice. Tara bumps the ball from a height of 3 feet above the ground with an initial upward velocity of 12 feet/second. at the same time, mallory serves the ball from a height of 3.25 feet above the ground with an initial upward velocity of 9 feet/second.
if x represents the number of seconds since each ball is passed and y represents the height of the ball, which system of equations models the projectile motion of the two balls? recall that the acceleration due to gravity is -32 feet/second
Answer:
The system of equation that models the projectile of the two balls is option;
C. y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
Step-by-step explanation:
The general equation for vertical (upward) motion under gravity is presented as follows;
h - h₀ = u·t + 1/2·g·t²
Where;
h = The final height reached
h₀ = The initial height
u = The initial velocity
g = The acceleration due to gravity ≈ -32 feet/second
t = The time taken
We can rewrite the above equation with different letters for the variables as follows;
h = y,
h₀ = y₀, and
t = x
Therefore, we have;
y - y₀ = u·x - 1/2 × 32 × x²
y = u·x - 1/2 × 32 × x² + y₀ = u·x - 16· x² + y₀
y = u·x - 16· x² + y₀ = -16·x² + u·x + y₀
y = -16·x² + u·x + y₀
For Tara, we have;
u = 12 feet/second
y₀ = 3 feet
Therefore, we get;
y = -16·x² + 12·x + 3
For Mallory, we have;
u = 9 feet/second
y₀ = 3.25 feet
Therefore, we get;
y = -16·x² + 9·x + 3.25
The correct option is therefore;
y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
factor g(x) =6x^3 +13x^2 -2x -1 if (2x + 3) is a factor.
PLEASE JUST HELP ITS ACTUALLY AN EMERGENCY I WILL GIVE 3K ON BLOXBURG FOR THIS
cut off the topright rectangle so there are 2 rectangles.
That will make it look like this
2x3=6
+
5x3=15
=
21
The area of that shape would be 21 square feet
21 square ft
u got 3K i only got 1K cuz i be spending it on my house and emotes and food ;-;
Meggie starts with 100$ in her account.she wants to deposit 5$ per week . write an equation in slope intercept form to represent this situation
Answer:
y = 5x + 100
Step-by-step explanation:
A farmer knows that a grocery store will reject a shipment of his vegetables if more than 4% of the vegetables contain blemishes. He inspects a large truckload of tomatoes to determine if the proportion with blemishes (p) exceeds 0.04. He selects an SRS of 150 tomatoes from the more than 2,000 tomatoes in the truck. Suppose that 8 tomatoes sampled are found to have blemishes. Which of the assumptions for inference about a proportion is violated, if any?
a. Large Counts: np > 10
b. Large Counts: n(1 – p) > 10
c. The sample is a random sample of the entire population.
d. 10% condition: the sample size is less than 10% of the population.
e. There do not appear to be any violations.
Answer:
Assumption A is violated
Step-by-step explanation:
x = number of blemishes = 8
n = sample size = 150
proportion = x/n = 8/150 = 0.0533
1. large counts: np> 10
= 150 * 0.0533 >10
= 7.995 > 10
this assumpton is obviously violated. 7.995 is not greater than 10
2. Large Counts: n(1 - p) > 10
150(1-0.0533)>10
150-7.995 > 10
142.005> 10
there is no violation. The assumption is satisfied
3. This assumption is satisfied. this is because the tomatoes were selected using simple random sampling.
4. 10% of the population = 0.1 * 2000 = 200
the sample size = 150
150 < 200
this assumption is satisfied
Which would be a good estimate for the tax on $97.95 if the tax is 9.5%?
$12
$10.50
$10
$8.50
In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows:
$1,589, $593, $1,223, $869, $423, $1,720, $708, $1,425, $922 and $308.
a. What is the mean and median change in the cost? (Explain how you obtain your answer.)
b. What is the five-number summary of the change in the cost? (Explain how you obtain your answer.)
c. What is the standard deviation of the change in the cost? (Explain how you obtain your answer.)
d. The middle 50% of the change in the cost is spread over what value? (Explain how you obtain your answer.)
e. What is the coefficient of variation of the change in cost? (Explain how you obtain your answer.)
f. What are the (absolute values of) the Z scores of the change in cost?
Answer:
1. mean = 980 median = $895.5
2. 308, 593, 895.5, 1425, 1720
3. 491.7978
4. 895.5
5. 50.28%
Step-by-step explanation:
1. mean $1,589+$593+$1,223+$869+$423+$1,720+$708+$1,425+$922+$308/10
= 9780/10
= $978
median
We first arrange the values in ascending order
308,423,593,708,869,922,1223,1425,1589,1720
number of observation is even so we pick the 2 values in the middle and divide by 2
= 869+922/2
= $1791/2
$895.5
2. five number summary of change
the botom half of th dta set = 308,423,593,708,869
minimum value = 308
n = 5
median = 593 = q1
from 1, q2 = median = $895.5
the upper half of data
922,1223,1425,1589,1720
n = 5
median = $1425
maximum value = $1720
the five number summary of change in cost is therefore
308, 593, 895.5, 1425, 1720
3. standard deviation
[tex]s =[\sqrt{x-barx} ]^{2} \frac{1}{n-1}[/tex]
bar x is the mean = 978
($1,589-978)²+ ($593-978)²+ ($1,223-978)²+ ($869-978)+ ($423-978)²+ $1,720-978)²+($708-978)²+ ($1,425-978)²+ ($922-978)²+ ($308-978)²
= 2176786
=[tex]\sqrt\frac{1}{10-1} {2176786} \\\sqrt{ \frac{2176786}{9}[/tex]
= [tex]\sqrt{241865.1}[/tex]
= 491.7978
4. middle 50% is spread over the median, which is 895.5
5. coefficient of variation
= s/bar x * 100
= 491.7978/978 * 100
= 49179.78/978
= 50.28%
6. z score = x - mean/s
x = 1589
= 1589-978/491.7978
= 1.2424
for x = 593
593-978/491.7978
= -0.7828
= 0.7828
for x = 1223
1223-978/491.7978
= 0.4982
for x = 869
869-978/491.7978
= -0.2216
= 0.2216
for x = 423
423-978/491.7978
= -1.1285
= 1.1285
x = 1720
1720-978/491.7978
z = 1.5088
for x = 708
708-978/491.7978
= -0.5490
= 0.5490
for x = 1425
1425-978/491.7978
= 0.9089
for x = 922
922-978/491.7978
= -0.1139
= 0.1139
for x = 308
308-978/491.7978
= -1.3624
= 1.3624
what is the value of angle x?
Answer:
x=66
Step-by-step explanation:
Hello There!
∠BAC ≅ ∠CDB because in a parallelogram opposite angles are congruent
So all we have to do is solver for ∠BAC
Remember the sum of the triangles angles is 180 so to find ∠BAC
we subtract the given angles (83 and 31) from 180
180-83-31=66
so ∠BAC = 66
like stated before
∠BAC≅∠BDC so if ∠BAC = 66 then x also equals 66
Answer:
x = 66
Step-by-step explanation:
x = 66 degree
In ΔVWX, x = 9.1 inches, w = 5.4 inches and ∠W=161°. Find all possible values of ∠X, to the nearest 10th of a degree
Answer:
NO POSSIBLE TRIANGLES
Step-by-step explanation:
Answer:
no possible triangles
Step-by-step explanation:
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be 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 = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/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 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
i need help ////////
Answer:
[tex]1\frac{1}{2}[/tex] miles = 7920 feet
2[tex]\frac{1}{2}[/tex] miles = 13200 feet
3[tex]\frac{1}{2}[/tex] miles = 18480 feet
4[tex]\frac{1}{2}[/tex] miles = 23760 feet
5[tex]\frac{1}{2}[/tex] miles = 29040 feet
6[tex]\frac{1}{2}[/tex] miles = 34320 feet
Explanation:
1 mile = 5280 feet
[tex]\frac{1}{2}[/tex] miles = 2640 feet
to convert miles into feet, multiply the whole numbers by 5280 and add 2640 to find your overall feet
2[tex]\frac{1}{2}[/tex] : 2 x 5280 + 2640 = 13200 ft
3[tex]\frac{1}{2}[/tex] : 3 x 5280 + 2640 = 18480 ft
4[tex]\frac{1}{2}[/tex] : 4 x 5280 + 2640 = 23760 ft
5[tex]\frac{1}{2}[/tex] : 5 x 5280 + 2640 = 29040 ft
6[tex]\frac{1}{2}[/tex] : 6 x 5280 + 2640 = 34320 ft
Please answer this :/
Answer:
-60
Step-by-step explanation:
-45+s=-105
s=-105+45
s=-60
Laura wants to learn more about her new high school. Which of the following is a statistical question Laura could ask?
A. What is the address of the school
B. Who is the principal
C. How old are the students at the school
D. Does the high-school have a jazz band
Answer:
D.
Step-by-step explanation:
There is no explanation
It costs $6 per hour for a park to water the grass. How much will it cost to water the grass for
7/3
hours?
Answer:
I think the answer is $14 hope this helps!
Step-by-step explanation:
What decimal is equivalent to 8/40?
Answer:
0.20
Step-by-step explanation:
8 divided by 40 equals 0.2
0.20 is the decimal is equivalent to 8/40.
What is decimal?A group of numbers between integers on a number line are known as decimals. They are merely an additional mathematical representation of fractions. Decimals allow us to express measurable quantities like length, weight, distance, money, etc. with greater accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point. The next place, which is (1/10)th or tenth place value, is (1/10) times smaller if we move immediately from the first place.
Given:
Fraction = 8/40
Now, simplifying the given fraction
8/40
= 8/( 8x 5)
= 1/5
=0.20
Hence, 0.20 is the decimal is equivalent to 8/40.
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if the circumference of a circle is 52 cm, what is the radius? round to the nearest tenth. PLESE HELP I DONT HAVE THAT MUCH TIME :(
Answer:
8.3
Step-by-step explanation:
Given,
Circumference of the circle = 52 cm
Therefore ,
By the problem,
[tex] = > 2\pi r = 52[/tex]
[tex] = > 2 \times 3.14 \times r = 52[/tex]
[tex] = > r = \frac{52}{3.14 \times 2} [/tex]
=> r = 8.2802547771
Rounded to nearest tenth,
=> r = 8.3 (Ans)
Are congruent triangles also similar?
Answer: yes they are
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal.
Answer:
Yes
Step-by-step explanation:
While congruent triangles are similar, similar triangles may not be congruent.
Quadrilateral GHIJ is dilated by a scale factor of 22 to form quadrilateral G'H'I'J'. What is the measure of side H'I'?
Answer:
[tex]H'I = 48[/tex]
Step-by-step explanation:
Given
See attachment for complete question.
From the attachment, we have:
[tex]GH=16.5[/tex]
[tex]HI =24[/tex]
[tex]IJ = 17[/tex]
[tex]JG =32.2[/tex]
[tex]k = 2[/tex] --- Scale factor
Required
Find H'I
The corresponding side of H'I is HI.
So:
H'I is calculated as:
[tex]H'I = k * HI[/tex]
This gives:
[tex]H'I = 2 * 24[/tex]
[tex]H'I = 48[/tex]
Answer I to j is 42
Step-by-step explanation:
The mean monthly water bill for 44 residents of the local apartment complex is $104. What is the best point estimate for the mean monthly water bill for all residents of the local apartment complex?
Answer:
$104
Step-by-step explanation:
The computation of the best point estimate for the mean monthly water bill is shown below:
Given that
The mean monthly water bill is $104
and, the number of residents is 44
based on the above information
The best point estimate would be equivalent to the mean monthly water bill i.e. $104
hence, the same would be considered
The distance around the outside of an apartment is 0.3 mile. Keira ran 0.1 of the distance during her lunch. How far did she run?
Answer:
0.1
Step-by-step explanation:
How much times does it take to put 0.3 into 5.7 whoever answers first and the most accurate gets brainliest
Answer:
what is the answer to this
Two optometrists (eye doctors) each compiled data from 10 different random samples. The table contains their respective data sets.
Doctor A Doctor B
Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts
745 643 102 763 651 112
726 634 92 736 625 111
769 670 99 735 622 113
765 658 107 759 624 135
756 636 120 748 631 117
742 624 118 756 621 135
757 641 116 765 653 112
748 655 93 761 647 114
770 649 121 768 646 122
738 629 109 761 646 115
Part A
Are there any noticeable outliers in either of the data sets? What does this mean about the best measures to use for center and variability?
Step-by-step explanation:
the answer is 19
Step-by-step explanation:
5.7/0.3=19
the measures of the angles of a triangle are shown in the figure below. solve for x
Answer:
Brainliest????
Step-by-step explanation:
X=23°