Starting salaries of 135 college graduates who have taken a statistics course have a mean of $42,650. Suppose the distribution of this population is approximately normal and has a standard deviation of $8,988. Using a 93% confidence level, find both of the following:
(NOTE: Do not use commas nor dollar signs in your answers.)
(a) The margin of error:
(b) The confidence interval for the mean μ:
Answer:
Hence, the margin error is [tex]1415.62189[/tex] and the confidence interval for the mean is [tex](41234.38,44065.62)[/tex].
Step-by-step explanation:
Given :
Sample size [tex]n=135[/tex]
Sample mean [tex]\bar{x}=\$42,650[/tex]
Standard deviation [tex]\sigma =\$8,988[/tex]
Confidence level is [tex]93\%[/tex]
(a)
The margin error [tex]=Z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n}}[/tex]
[tex]\because \alpha =1-[/tex]confidence level
[tex]\Rightarrow \alpha=1-93\%=1-0.93[/tex]
[tex]\Rightarrow \alpha=0.07\Rightarrow \frac{\alpha}{2}=0.035[/tex]
[tex]Z_{\frac{\alpha}{2}}=Z_{0.035}=1.83[/tex] from the [tex]z-[/tex]table
Now, the margin error[tex]=1.83\times \frac{8988}{\sqrt{135}}[/tex]
[tex]=1415.62189[/tex]
(b)
The confidence interval for the mean [tex]\mu\\[/tex] :
[tex](\bar{x}-\text{margin error},\bar{x}+\text{margin error})[/tex]
[tex]\Rightarrow (\bar{x}-1415.62189,\bar{x}+1415.62189)[/tex]
[tex]\Rightarrow (42650-1415.62189,42650+1415.62189)\\\Rightarrow (41234.38,44065.62)[/tex]
Which values are equivalent to the fraction below? Check all that apply.
38
30 끓
38
O A. 3-2
2
B. (
48
O c.
O D.
1
9
O E. 314
OF. 32
The value are equivalent to the fraction below is 3^2, the correct option is F.
What is a fraction?
A fraction represents a part of a number or any number of equal parts.
A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given that;
3^5/3^8
Now,
A. 3^-3: This is equivalent to 1/3^3 by moving the negative exponent to the denominator. Then we can simplify 1/3^3 to 1/27 by multiplying 3 by itself 3 times. This is not equivalent to 3^5 / 3^8, since 1/27 is not equal to 3^-3.
B. (1/3)^2: This is equivalent to 1/3^2 by applying the exponent to the numerator and denominator. Then we can simplify 1/3^2 to 1/9 by multiplying 3 by itself 2 times. This is not equivalent to 3^5 / 3^8, since 1/9 is not equal to 3^-3.
C. (1/3)^8: This is equivalent to 1/3^8 by applying the exponent to the numerator and denominator. Then we can simplify 1/3^8 to 1/6561 by multiplying 3 by itself 8 times. This is not equivalent to 3^5 / 3^8, since 1/6561 is not equal to 3^-3.
D. 1/9: This is equivalent to (1/3)^2 by writing it as a power of a fraction. Then we can apply the same steps as in option B and get back to 1/9. This is not equivalent to 3^5 / 3^8, since 1/9 is not equal to 3^-3.
E. 3^14: This is not equivalent to 3^5 / 3^8, since it has a positive exponent and does not have a fraction. We cannot simplify it further without changing its value.
F. 3^2: This is not equivalent to 3^5 / 3^8, since it has a positive exponent and does not have a fraction.
Therefore, by the given fraction the answer will be 3^2.
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A pack of 4 chocolate bars costs £1.20
What is the price per unit?
what is it?
Answer:
0.30 you divided the total by the number of units which is 4
Answer:
£ 0.3
Step-by-step explanation:
Given that , a pack of 4 chocolates costs £1.20. We need to find cost of one chocolate .
We can simply use Unitary Method here ,as ,=> 4 chocolates costs £1.20 .
=> 1 chocolate will cost £1.20/4 = £ 0.3
Hence the cost of unit is £ 0.3When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3?
A. 1:8
B. 8:1
C. 1:9
D. 9:1
Answer:
A
Step-by-step explanation:
The successful results are
1 1
2 1
1 2
2 2
So the formula is probability of winning to probability of losing
Probability of winning =
4/36 = 0.1111111
Probability of losing =
32/36 = 0.88888888
So the odds are expressed as 0.111111 / 0.88888 = 1 in 8
A
If you ever intend to bet on horses at the track, this is a very good problem to understand.
Place and show would be very handy too, but that goes beyond this question.
There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present in simplified form
plz plz plz plz help me
Answer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden
1. In reviewing your Summary Account Activity (#1), you notice FEES
CHARGED of $69.45. This fee was assessed on your account for the
following reasons EXCEPT... *
Answer: Annual Fee
Step-by-step explanation:
The options include:
a. Late Payment Fee
b. Balance Transfer Fee
c. Cash Advance Fee
d. Annual Fee
The reason for the fee of $69.45 charged will be due to the late payment fee which is as a result of failing to make a payment by a due date.
Other reasons for the fee include the balance transfer fee which is the charged by the lender in order to transfer an existing debt that's incurred by another lender. The cash advance fee is also another reason for the charges.
Therefore, the correct answer to the question is annual fee.
Plz help me well mark brainliest if correct................?
Answer:
B. 8cm*12cm
Step-by-step explanation:
Area is the product of the two sides:
6*16 = 96
8*12 = 96
10*10 = 100
Perimeter is the sum of all four sides:
6+16+6+16 = 44
8+12+8+12 = 40
The answer is B. 8cm*12cm
Plsss help. giving extra points if correct.
Given the system of equations, what is the solution?5x - 4y = 7x = 5 - 3/2y
9514 1404 393
Answer:
(x, y) = (61/23, 36/23)
Step-by-step explanation:
We assume you intend the equations to be ...
5x -4y = 7x = 5 -3/2yThen in general form, they are ...
5x -4y -7 = 0
2x +3y -10 = 0
The solution using the "cross multiplication method" is ...
1/(15 +8) = x/(40+21) = y/(-14 +50)
(x, y) = (61/23, 36/23)
_____
Comment on "cross multiplication method"
When the coefficients from the general form equations are written as a 2×4 array with the first and last columns the same ...
[tex]\left\{\begin{array}{cccc}5&-4&-7&5\\2&3&-10&2\end{array}\right\}[/tex]
the solution is 1/d1 = x/d2 = y/d3, where d1, d2, d3 are the determinants of successive pairs of columns.
d1 = (5)(3) -(2)(-4)d2 = (-4)(-10) -(3)(-7)d3 = (-7)(2) -(-10)(5)5n - 12 = -3n + 4
30 points
Answer:
n = 2
Step-by-step explanation:
5n - 12 = -3n + 4
5n + 3n = 4 + 12
8n = 16
n = 2
Answer:
5n-12=-3n+4
5n+3n=4+12
8n=16
n=16/8
n=2
Step-by-step explanation:
Adam can buy 3 buckets of popcorn and 3 drinks for $25.50. Tanya
can buy 2 buckets of popcorn and 3 drinks for $19.50. How much
is one bucket of popcorn?
$25.50
O $4.75
$6.00
O $3.00
Answer:
Let price of drink be x
price of tub y
You have 4x+2y=32.5 (1) and
x = y -3.5 (2)
Plug for x from (2) into (1):
4(y-3.5) + 2y = 32.5
4y -14 +2y = 32.5
6y = 14+32.5
y = (46.5)/6 = $7.75 the price of tub
x= y-3.5 = 7.75 - 3.5 = $4.75
Is 3.37 less than 3.368
Answer:
no
Step-by-step explanation:
Answer:
it's not
Step-by-step explanation:
What is the name of this circle?
Circle
Answer:
Minor Sector
Step-by-step explanation:
Ben found 6 tops to add to his 7 tops in his collections. he then had a competition with his friends and quadrupled his tops. I Have To Write a numerical expression to model this situation without performing any operations but I'm Just So Confused Can You Help Me Please.
Answer:
gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
Step-by-step explanation:
What is the critical value t* which satisfies the condition that the t distribution with 14 degrees of freedom has probability 0.35 to the right of t*
Answer:
[tex]t_{0.35,14}= 0.3933306[/tex]
Step-by-step explanation:
From the question we are told that:
Degree of freedom [tex]df=14[/tex]
Significance Level [tex]\alpha=0.35[/tex]
Generally the expression for critical value t is mathematically given by
[tex]t_{\alpha,df}[/tex]
[tex]t_{0.35,14}[/tex]
Therefore From Students T Value Table
[tex]t_{0.35,14}= 0.3933306[/tex]
[tex]T-Value (right-tailed): 0.3933306[/tex]
If f(x)= 1/x+2 and a>3, which of the following could be f(a)
A =1/2
B = 1/3
C = 1/4
D = 1/6
The equivalent value of the function is f ( a ) = ( 1/6 ) , when a > 3
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 1 / ( x + 2 )
Now , the value of x > 3
So , the value of f ( x ) = f ( a )
And , when x > 3
f ( 4 ) = 1 / ( 4 + 2 )
f ( 4 ) = 1 / 6
Hence , the function is f ( 4 ) = 1 / 6
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The equation V equals pi r squared h, where r represents radius and h represents height, is used to find the volume of a ________.
Answer:
Volume of a cylinder.
Step-by-step explanation:
The given equation is :
[tex]V=\pi r^2 h[/tex]
Where
r is the radius
h is the height
This equation is used to find the volume of a cylinder.
For example, a cylinder having radius of 7 units and height of 10 units, its volume will be :
[tex]V=\dfrac{22}{7}\times 7^2\times 10\\\\V=1540\ \text{unit}^2[/tex]
So, the given equation is used to find the volume of a cylinder.
can someone pls give me an explanation and answer?
Answer:
x=50
Step-by-step explanation:
It is a line so it should be 180 degrease. You already have two of the angles and to find the third (x) you just need to subtract them from 180. 180-105=75, and 75-25 is 50, so x is 50.
Answer: x=50 degree
Step-by-step explanation: angle in a straight line is equal to 180 degrees.
Given;
25 degrees &
105 degrees.
180– (105+25)
180– 130
= 50degrees
Which postulate or theorem proves that AABC AXYZ?
Answer:
D. ASA
Step-by-step explanation:
In the figures given,
<A and <B in ∆ABC are congruent to corresponding angles <X and <Y in ∆XYZ in ∆XYZ.
Also, an included side AB in ∆ABC is congruent to a corresponding included side XY in ∆XYZ.
According to the ASA triangular theorem, two ∆s are congruent to each other when they have two corresponding angles in each of the triangles that are congruent to each other and an included side that is also congruent to each other.
Therefore, ∆ABC is congruent to ∆XYZ based on the ASA theorem.
How many cubes with side lengths of 1/4 cm does it take to fill the prism?
Step-by-step explanation:
All you do is add them all up but tbh that picture could use some work and maybe when you fix it ill help you then .So the square unit of this picture is 6
The difference of x and y is the same as 3 times the sum of x and 2
Answer:
x - y = 3(x + 2)
x - y = 3x + 6 is the simplified answer and is also correctStep-by-step explanation:
The difference of x and y is the same as 3 times the sum of x and 2
x - y = 3(x + 2)
x - y = 3x + 6
Answer:
spoke out of term and with no true option.
Isabel split 5/8 pounds of candy among 4 people. What is the unit rate in pounds per person?
Answer:
0.15
Step-by-step explanation:
Because 5/8 divided by 4 is 0.15.
please find the value of X for number 4 5 and 6 thank you :)
Answer:
4. x = 6
5. x = 31
6. x = 34
Step-by-step explanation:
4. vertical angles
- 36/6 = 6
5. supplementary angles
180 - 56 = 124
124/4 = 31
6. complementary angle
90 - 22 = 68
68/2 = 34
Answer:
4. x = 6°
5. x = 31°
6. x = 34°
Step-by-step explanation:
4. Vertical Angles theorem states that the two opposite angles formed by 2 intersecting lines are congruent.
6x = 36°
x = 36 / 6
x = 6°
5.
180° - 56° = 4x
124° = 4x
x = 31°
6.
90° - 22° = 2x
68° = 2x
x = 34°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Can someone plz help it’s my final
Answer:
Option F, y = 2x + 5 would be the right answer
Hope this helps!
Answer:
Option F would be correct.
Hope this helps<3
Have a good day :)
~Amy
find the probability that leap year, selected at random, will contain 53 Sundays.
Answer:
the answer is Hence, a leap year has 52 Sundays
Step-by-step explanation:
I hope this helps
x plus 1 > 3
The souliton is
Answer:
x > 2
Step-by-step explanation:
x + 1 > 3
Subtract 1 from both sides
x + 1 - 1 > 3 - 1
x > 2
Find the missing side
What is the length of a 50-inch TV that has a width of 27 inches?
What is the area of this TV?
A random sample of 11 fields of rye has a mean yield of 20.1 bushels per acre and standard deviation of 7.66 bushels per acre. Determine the 80% confidence interval for the true mean yield. Assume the population is approximately normal. Round your answer to one decimal place.
Answer:
17.1≤x≤23.1
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as;
CI = x ± z*s/√n
x is the mean yield = 20.1
z is the 80% z-score = 1.282
s is the standard deviation = 7.66
n is the sample size = 11
Substitute
CI = 20.1 ± 1.282*7.66/√11
CI = 20.1 ± 1.282*7.66/3.3166
CI = 20.1 ± 1.282*2.3095
CI = 20.1 ±2.9609
CI = (20.1-2.9609, 20.1+2.9609)
CI = (17.139, 23.0609)
hence the required confidence interval to 1dp is 17.1≤x≤23.1