a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.
b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.
d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.
e) The value of C = 81.51.
What is meant by Normal probability distribution?When the distribution is normal, we use 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 calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
The Central Limit Theorem establishes 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].
The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.
This means that [tex]$\mu=75, \sigma=15$[/tex]
a. By the Central Limit Theorem, it will be approximately normal, with expected value [tex]$\mu=75$[/tex] and standard deviation [tex]$s=\frac{15}{\sqrt{25}}=3$[/tex]
b. The p-value of Z when X = 82.14 subtracted by the p-value of Z when X = 70.14.
X = 82.14
[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]
By the Central Limit Theorem
[tex]$Z=\frac{X-\mu}{s}$[/tex]
[tex]$Z=\frac{82.14-75}{3}$[/tex]
Z = 2.38
Z = 2.38 has a p-value of 0.9913.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$Z=\frac{70.14-75}{3}$[/tex]
Z = -1.62 has a p-value of 0.0526
0.9913 - 0.0526 = 0.9387
0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c. This is 1 subtracted by the p-value of Z when X=82.68.
[tex]$Z=\frac{X-\mu}{s}[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{82.68-75}{3} \\[/tex]
Z = 2.56 has a p-value of 0.9948.
1 - 0.9948 = 0.0052
0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68
d. This is the p-value of Z when X=78.69. So
[tex]$&Z=\frac{X-\mu}{s} \\[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{78.69-75}{3} \\[/tex]
Z = 1.23 has a p-value of 0.8907
0.8907 = 89.07 % probability that the average aptitude test in the sample will be less than 78.69.
e. Find a value, C, such that P((x>C) = 0.015.
This is X when Z has a p-value of 1 - 0.015 = 0.985.
So X when Z = 2.17.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$2.17=\frac{X-75}{3}$[/tex]
X - 75 = 3 × 2.17
X = 81.51
Therefore, the value of C = 81.51
The complete question is:
MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
a. What are the expected value, the standard deviation, and the shape of the sampling distribution of?
b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?
c. What is the probability that the average aptitude test in the sample will be greater than 82.68?
d. What is the probability that the average aptitude test in the sample will be less than 78.69?
e. Find a value, C, such that P(( x>C) = .015.
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question allistair throws a biased six-sided dice. the probability of getting a 6 with this dice is 0.4. the other numbers are equally probable. if he throws the dice 3 times, what is the probability that he gets 5, 3, and 2 in this order?
The probability that he gets 5, 3, and 2 in this order is 0.92, 0.52, and 0.32 respectively.
The possibility of rolling a 6 with these dice is 0.4, according to the question. The possibility of rolling a 1 through 5 on the dice is also the probability of not obtaining a 6.
a) Chance of receiving 5:
P(6) + Q(6) = 5
Q(6) = 5 - P(6)
Q(6) = 5 - 0.4
Q(6) = 4.6
The probability of obtaining 5 to 5 is 4.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 4.6
The first five numbers have an equally likely probability.
P(1) = 4.6 ÷ 5
P(1) = 0.92
b) Probability of getting 3:
P(6) + Q(6) = 3
Q(6) = 3 - P(6)
Q(6) = 3 - 0.4
Q(6) = 2.6
The probability of obtaining 3 to 5 is 2.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 2.6
The first five numbers have an equally likely probability.
P(1) = 2.6 ÷ 5
P(1) = 0.52
c) Probability of getting 2:
P(6) + Q(6) = 2
Q(6) = 2 - P(6)
Q(6) = 2 - 0.4
Q(6) = 1.6
The probability of obtaining 2 to 5 is 1.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 1.6
The first five numbers have an equally likely probability.
P(1) = 1.6 ÷ 5
P(1) = 0.32
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explain how you got it please
The simplest form of the expression as we have it is; (-4x^4z^2)(2xy^3z^2)
What does it mean to simplify?When we are asked to simplify, what we are asked to do is to write the expression that we have in a form that is simplest. That is, we should put the expression in a form that there would not be any simpler presentation of the expression.
We have;
(-2x^2z)^2(2xy^3z^2)
Then we now have to deal with the exponent outside the bracket;
(-4x^4z^2)(2xy^3z^2)
Thus, we now have the expression in the simplest form that it can take and it can not be further broken down.
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3/4 - (-1/2) as a fraction
Answer:1/4
Step-by-step explanation:
what is the type of angle are <1 and <14??????????
1° and 14° are acute angles.
An acute angle is one that is less than 90°, or one that is between 0° and 90°.
The opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90° and less than 180°. It is the angle that is between 90° and 180°.
90° is the standard for a right angle. Any angle that is less than 90° is called acute, and any angle that is larger than 90° is called obtuse.
∠1 and ∠14 are less than 90° therefore, they are acute angles.
Correct question :
What type of angle are 1° and 14°?
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please dont use any big words & give an essay explanation
We want to create a real-life reasonable problem in which we can apply the laws of exponents.
Using a compound interest example;
Word Problem:
Calculate the final value of a $2,000 investment in an account with a 5% interest compounded Quarterly for 5 years.
Solving the word problem;
We have the following parameters;
[tex]\begin{gathered} \text{ Principal P = \$2,000} \\ \text{Rate r = 5\%} \\ \text{Time t = 5 years} \\ \text{ Number of times compounded n = 4} \end{gathered}[/tex]Recall that the formula for compound interest is;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=2000(1+\frac{0.05}{4})^{4(5)} \\ F=2000(1+0.0125)^{20} \\ F=2000(1.0125)^{20} \\ F=2000\times(1.0125)^{20} \\ F=\text{ \$2,564.07} \end{gathered}[/tex]Therefore, the solution to the problem is;
The final
I just want the answer :)
The diagonals of a rectangle are congruent, so RT = SU, that is
3x + 8 = 6x - 4 (subtract 4x from both sides)
3x + 8 = 6x - 4
Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8
Simplifying the above equation, we get
3x = 6x-12
Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x
Simplifying the above equation, we get
-3x = -12
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]
x = 4
Then, R T= 3x + 8 = 3(4) + 8 = 20
The diagonals bisect each other, then
RV = 0.5 × 20 = 10
∠ RVU = ∠ SVT = 54° ( vertical angles)
RV = UV ( diagonals are congruent and bisect each other)
Then Δ RVU is isosceles with base angles congruent, then
∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.
In the rectangle, RV = 3x+8, SV = 6x-4, and ∠ VRS = 54° then the value of x is 4 and ∠ VUR is 66°.
How to estimate the value of x?The diagonals of a rectangle are congruent, so RT = SU, that is
3x + 8 = 6x - 4 (subtract 4x from both sides)
3x + 8 = 6x - 4
Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8
Simplifying the above equation, we get
3x = 6x-12
Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x
Simplifying the above equation, we get
-3x = -12
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]
x = 4
Then, R T= 3x + 8 = 3(4) + 8 = 20
The diagonals bisect each other, then
RV = 0.5 × 20 = 10
∠ RVU = ∠ SVT = 54° ( vertical angles)
RV = UV ( diagonals are congruent and bisect each other)
Then Δ RVU is isosceles with base angles congruent, then
∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.
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is the ordered pair (-8 1) a solution to the equation y=1/2x-3
Answer: No.
Step-by-step explanation:
To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.
y = 1/2x - 3
(1) = 1/2(-8) - 3
1 = -4 - 3
1 ≠ -7
This ordered pair is not a solution.
Karen made costumes for the annual school play. She used a total length of928.8 in of blue fabric. The fabric came in 2 rolls that each had the samelength. How much fabric was in each roll? Write your answer in yards.Use the table of conversion facts as necessary, and do not round your answer.=Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)ydX 5 ?
Part 1. A cardboard box, which weighs 0.6 pound when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6 + 15b + 4 = 25.6.
Select all equations that are also equivalent to 0.6 + 15b + 4 = 25.6.
Responses
Equation A: 15b + 4 = 25.6
Equation A: 15b + 4 = 25.6
Equation B: 15b + 4 = 25
Equation B: 15b + 4 = 25
Equation C: 3(0.6 + 15b + 4) = 76.8
Equation C: 3(0.6 + 15b + 4) = 76.8
Equation D: 15b = 25.6
Equation D: 15b = 25.6
Equation E: 15b = 21
Part 2. To solve the equation 7.5d = 2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side.
a. Will both moves lead to the solution? Explain your reasoning.
b. What is the solution?
Part 3. The equation 4(x – 2) = 100 is a true equation for a particular value of x. Explain why 2(x – 2) = 50 is also true for the same value of x.
2(x -2) = 50 is also true for the same value of x.
Given,
Part 1:
When a cardboard box is empty, its weight is 0.6 pounds.
It is filled with 15 bags of beans and a 4-pound bag of rice.
The total weight of the box and the contents inside it is 25.6 pounds.
Let the weight of 15 bean bags is 15b. The given scenario can be represented by the equation as follows :
0.6+15b+4=25.6 ....(A)
Taking like terms together,
15b=25.6-0.6-4 ...(1)
15b = 21 ....(2)
Equation (1) or (2) can be the equivalent equation for the equation (A).
Part 2:
Solve the equation:
7.5d = 2.5d, Lin divides each side by 2.5d,
and Elena subtracts 2.5d from each side.
Now, 7.5d/2.5d = 2.5d/2.5d
3 = 1
It is not equal, There is no solution.
a. 7.5d - 2.5d = 2.5d - 2.5d
5d/5 = 0/5
b. What is the solution ?
Solution is d = 0
Part 3:
Given,
The equation 4(x - 2) = 100 is a true equation for a particular value of x.
Explanation: The basic property of the equation is that if you multiply or divide both sides of the equation by the non-zero whole , the equation still holds.
In the Equation : 4 (x - 2) =100 divide by 2 on both sides because 2 is common factor of (4,10)
So, 4(x - 2) =100
1/2 x 4(x-2) = 1/2 x 100
= 2(x-2) = 50
Above all, 2(x -2) = 50 is also true for the same value of x.
Hence, 2(x -2) = 50 is also true for the same value of x.
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Xavier has a bag of 20 marbles. 8 are blue, 7 are red, and 5 are green. Xavier pulls out a marble, records what color it is, and puts it back. He then selects another marble and records its color What is the probability of pulling out a blue marble and then a green marble?
Answer:
0.1
Step-by-step explanation:
chance of pulling out a blue marble can be described as 8 equally probable outcomes (blue marbles) out of 20 equally probable outcomes (all marbles).
Similarly, the chance of pulling out a green marble is 5 out of 20.
In total, we have 8*5 (combinations of blue then green) outcomes out of 20*20 (any two marbles):
8*5 / (20*20) = 40 / 400 = 1/10 = 0.1
Perimeter and area polynomials
The combined perimeter of
2b (14y - 12)
2c (18y + 4)
2d (14y - 16), is
[tex]P=14y-12+18y+4+14y-16[/tex]Add the like terms
[tex]\begin{gathered} P=(14y+18y+14y)+(-12+4-16) \\ \\ P=46y+(-24) \\ \\ P=46y-24 \end{gathered}[/tex]The combined perimeter is (46y - 24)
The combined area of
1b (10y^2 - 27y +5)
1c (20y^2 + 11y - 3)
1d (12y^2 -24y), is
[tex]A=10y^2-27y+5+20y^2+11y-3+12y^2-24y[/tex]Add the like terms
[tex]\begin{gathered} A=(10y^2+20y^2+12y^2)+(-27y+11y-24y)+(5-3) \\ \\ A=42y^2+(-40y)+2 \\ \\ A=42y^2-40y+2 \end{gathered}[/tex]The combined area is (42y^2 - 40y + 2)
You begin with $25 in a saving account and $50 in a checking account. Each week you deposit $5 into saving and $10 into checking. After how many weeks is the amount in checking twice the amount in saving?
Answer:
1 week
Step-by-step explanation:
After 1 week
Saving account: $25 + $5 = $30
Checking amount: $50 + $10 = $60
30 x 2 = 60
So it's 1 week
PLEASE HELP ME ASAP.
Please help!
4|x+7| < 8
3
so this is a
You also will not know precisely how many sentences will appear in the random paragraph. But some piano roll artists made a name with pieces that could not possibly be played by an precise individual. Most of his research deal with difficult meters and polyrhythms. Many include distinct voices enjoying the identical line at different tempos, usually in odd ratios. On top of this, most of the traces themselves tend to be highly dissonant and exhausting to actually play. Someday we might come nose to nose with pure house, that could presumably be a nothingness waiting to be filled.
If the mean weight of 3 outfielders on the baseball team is 192 lb and the mean weight of the 6 other players is 228 lb, what is the mean weight of the 9-person team?
Answer:
Step-by-step explanation:
If the mean weight of 3 outfielders on the baseball team is 194 lb and the mean weight of the 6 other players is 229 lb, what is the mean weight of the 9
what does x =?
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t - 2 < 21 solve the inequality for t simplify your answer as much as possible
Answer:
t < 23
Step-by-step explanation:
t - 2 < 21
Step 1 : Add 2 on both sides.
t - 2 + 2 < 21 + 2
t < 23
Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E′F′G′. Which statement is true about the dilation?
Answer:Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation? segment EG ≅ segment E prime G prime. The slope of segment EF is the same as the slope of segment E prime H prime.
Step-by-step explanation:
ickets to the zoo cost $15 for adults and $10 for children. The school has a budget of $300 for the field
trip. An equation representing the budget for the trip is 15x+10y = 300.
a. With a budget of $300, determine if 21 students and 6 adults can go to the zoo. Explain how you
know.
b. If there are four adults who need tickets, what is the maximum number of students who can go to
the zoo while staying within the school budget? Show or explain your reasoning.
c. Solve the equation15x+10y = 300 for y.
Answers: lol sorry very long answer
part a answer: Yes, because if we substitute the variables, the equation will be 15(6) + 10(21) = 300. Simplifying this will be 90 + 210 = 300. And since 90 + 210 does equal 300, 21 students and 6 adults can go to the zoo
part b answer: 24 students. Using the equation 15x + 10y = 300, we can find out the maximum number of students who can go to the zoo. First we can substitute x for 4 because that's how many adults who need the tickets. The equation will now be 15(4) + 10y = 300. Simplifying this will be 60 + 10y = 300. Now we can subtract 60 on both sides to isolate the y term. The equation will be 10y = 240. Divide each side by 10 to find out what y is and we get y = 24. So if 4 adults go the zoo, up to 24 students can go.
part c answer: y = 30 - 1.5x. To solve 15x + 10y =300, we first need to move 15x to one side of the equation. To do this we will subtract it on both sides. The equation is now 10y = 300 -15x. Then you will divide 10 on both sides to find out what y is. y = 30 - 1.5x.
The quotient of 2 and a number.
Answer:
it should be the variable divided by 1. For example, x/2.
The demand for a certain product is given by p+3q=315, and the supply for this
product is given by p-7q = 65, where p is the price and q is the number of
products. Complete parts (a) and (b) below.
a. Find the price at which the quantity demanded equals the quantity supplied.
$
b. Find the equilibrium quantity.
In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260." option (b) is answer.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.a. The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by p-7q = 65 or, q = (p- 65)/7
The price at which the quantity demanded equals the quantity supplied is given by
315 - p/3 = p - 65/7
7( 315 - p ) = 3( p - 65 )
2405 - 7p = 3p - 195
2405 + 195 = 3p + 7p
2600 = 10p
p = 2600/10 = 260
Thus, the required price is $ 260.
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An engineer is designing the parking lot shown below for a local grocery store. The parking spaces are marked with lines where XD←→∥TZ←→∥YF←→∥LP←→ and WC←→− is a transversal. m∠CNL=(6x−17.6)°, m∠FBH=(12y−22)°, and m∠THR=(3x+29.2)°
Answer:
Step-by-step explanation:
Write an integer that lies between-7.73 & -6.41, what is the answer?
Which sequence shows the numbers in order from least to greatest?
A. |-8.23| < 8 1/5 < 8.3
B. 8 1/5 > 8.3 > |-8.23|
C. 8 1/5 < |-8.23| < 8.3
D. 8.3 < |-8.23| < 8 1/5
The sequence that shows the numbers in order from least to greatest is A. |-8.23| < 8 1/5 < 8.3
How to illustrate the information?It's important to note that arranging numbers from the least to the greatest simply means ascending order.
In this case, it's vital to note that the negative value is the smallest. Then 8 1/5 is 8.2. This conea after. The greatest number is 8.3 since it's the biggest.
In conclusion, the correct option is A.
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enter 2 Expressions that represent the retail price of the clothes you see for your variable and exclusive clothing boutiques quadruples the price of the items it purchases for resale.
Explanation
Step 1
Let
c represent the original price
if the boutiques quadruples the price of the items it purchases for resale.then
[tex]\begin{gathered} \text{new price=4}\cdot c \\ percentage \\ 4=4\cdot\frac{100}{100} \\ 4=\frac{400}{100} \\ 4=400\text{ per cent} \end{gathered}[/tex]400 percent
Step 2
expressions
[tex]\begin{gathered} \text{new price=4}\cdot c \\ \text{new price= 400 percent of C} \end{gathered}[/tex]4c and 400%c
I hope this helps you
Which compound inequality is equivalent to the absolute value inequality lbl >6?
hand
Answer:
b > 6, b < -6
Step-by-step explanation:
Hello!
Using absolute value rules:
|b| > 6; b > 6, b < -6The compound inequality is as follows: b > 6, b < -6
This makes sense because all values turn positive in the asbolute value. So a number that is negative and less than -6 (say -7), would turn positive to be 7, which is greater than 6.
And any number already greater than 6 will always be greater than 6.
The perimeter of a rectangular garden is 72 meters. The length is 6 meters longer than
twice the width. Find the dimensions of the garden.
P = 2L + 2W
P = 72
L = 12W (that's an odd way to put it -- 6x 2x)
P = 2(12W) + 2W
P = 24W + 2W
72 = 26W
W = 2.769
[x-6] +4 =10 solve for X
Answer:
x=12
Step-by-step explanation:
(x-6)=6
x=12
If y varies inversely as x, and y = 22 when x = 6, find x when y = 15.
Step-by-step explanation:
y varies INVERSELY as x.
that means
y = k/x
therefore,
22 = k/6
k = 22×6 = 132
and then, when y = 15
15 = 132/x
15x = 132
x = 132/15 = 8.8
If a = 3 and b = -5- 2i, then find the value of the a³b in fully simplified form.
The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."
What is complex numbers?Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").
Here,
The value of a³b
=3³(-5-2i)
=27(-5-2i)
=-135-54i
For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.
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