Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.
(a) are within + 1.5 standard deviations of the mean?
(b) are more that 2.5 standard deviations above the mean?
(c) are more that 3.5 standard deviations away from ( above or below) the mean?
Answers
and σ the standard deviation = 1
a) P(0 ≤ Z ≤ 1.5) →P(Z=1.5) - P(Z=0)
P(0 ≤ Z ≤ 1.5)= 0.9332 - 0.5 = 0.4322
b) P(Z ≥ 2.5) →P(Z=2.5) = 1- P(Z=2.5)
P(Z ≥ 2.5) = 1- 0.9938 = 0.0062
c) P(Z≥ 3.5) = 1- P(Z = 3.5) = 0
OR P(Z≤ 3.5) = 0
The required percentages are:
(a) 86.64%
(b) 0.62%
(c) 0.04%
With the use of standard normal table, we can find the required percentage, such as:
(a)
→ [tex]P( -1.5<z<1.5)= P( z <1.5)- p( z < -1.5)[/tex]
[tex]= 0.9332-0.0668[/tex]
[tex]= 0.8664[/tex]
[tex]= 86.64[/tex] (%)
(b)
→ [tex]P( z >2.5)=0.0062[/tex]
[tex]= 0.62[/tex] (%)
(c)
→ [tex]P( z < -3.5) + p( z > 3.5) = 0.0002+0.0002[/tex]
[tex]= 0.0004[/tex]
[tex]=0.04[/tex] (%)
Thus the above approach is right.
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Related Questions
A 34 - m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answers
34^2 + b^2 = 36^2
1156 + b^2 = 1296
b^2 = 1296 - 1156
b2 = 140
b = sqrt 140
b = 11.8 m <==
Answer:
Length of the shadow is 11.8 meters.
Step-by-step explanation:
In the figure attached,
AB is a 34 meter tall building casting a shadow BC.
Let the measure of BC = x meters
It is given that the distance between A and C is 36 meters.
To find the length of BC we will apply Pythagoras theorem in the triangle.
AB² + BC² = AC²
(34)² + x² = (36)²
1156 + x² = 1296
x² = 1296 - 1156
x² = 140
x = √140
x = 11.832 meters
≈ 11.8 meters
Therefore, length of the shadow will be 11.8 meters.
can someone pls answer
Answers
9y = -11x +36
y = -11/9 +4
y = 4
Write the ratio of 4 teachers to 134 students in simplest form.?
Answers
So it would be 2 teachers to 67 students
divide 134/4 = 33.5 that would be 1/33.5
since you can't have .5 student, multiply each side by 2
33.5*2 = 67
so 2/67 would be the simplest form using whole numbers
A league of 19 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)
Answers
Given the function value of the acute angle find the other five trigonometric function values cos a= Sqrt 7/7
Answers
[tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ cos(a)=\cfrac{\sqrt{7}}{7}\cfrac{\leftarrow adjacent}{\leftarrow hypotenuse}\quad \textit{now, let's find the \underline{opposite}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm\sqrt{7^2-(\sqrt{7})^2}=b\implies \pm\sqrt{49-7}=b\implies \pm\sqrt{42}=b \\\\\\ \textit{now, which is it, the + or -? well, we're in the 1st quadrant, is }\sqrt{42} [/tex]
[tex]\bf \textit{now that you know all three sides, just plug them in} \\\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}[/tex]
2.5 million deaths per is how many deaths per minute
Answers
For what value of a does 9=(1/27)^a+3
Answers
[Note: Please review rules of PEMDAS.
The question posted as is means
9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
The value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
Solving indical equationsThe given equation is:
[tex]9=(\frac{1}{27})^{a+3}[/tex]
This can be rewritten as:
[tex]9=27^{-1(a+3)}[/tex]
Which can be further simplified as:
[tex]3^2=3^{-3(a+3)}[/tex]
Since the bases are equal, they cancel out
The equation becomes:
2 = -3(a + 3)
2 = -3a - 9
2+9 = -3a
-3a = 11
a = -11/3
Therefore, the value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
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What is the value of this expression? (-8)3
Answers
Answer:
Step-by-step explanation:
You could, if you wished, take out the negative sign, obtaining -(8)(3). That would be -24.
But if you meant exponentiation, it would look like (-8)^3, or (-8)³, and that would be equal to 8*8*8 = 512.
Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = –3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = –3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.
Answers
For Tucker's solution, let's say at x=-3 the value for y is 4, and at x=3, the value of y is still 4, then the average rate of change or slope is 0. Note that the slope of the curve is Δy/Δx. Since there is no change for Δy, the slope is zero.
For Karly's solution, even if the curve travels high or low but would have the same elevation of x=-3 and x=3, the average rate of change is still zero. It is actually just same with Tucker's but Karly just verbalizes her solution that was observed visually.
If you flipped a fair coin 6 times and got 6 heads, what would be the probability of getting a head on the next toss? enter your answers as fractions.
Answers
If it is from the first attempt, to toss 7 heads in a row, the probability
= ½ × ½ × ½ × ½ × ½ × ½ × ½
= 1/128
Erica bought 3 1/2 yards of Frederick if she uses 2/3 of the fabric to make a curtain how much will she have left
Answers
3 1/2
3*2=6
6+1=7
3 1/2 as an improper fraction would be 7/2
Now we multiply the fractions.
7/2*2/3
7*2=14
2*3=6
14/6
Now we can convert the improper fraction back into a proper fraction.
How many times does 6 fit into 14? 2 with a remainder of 2
The Fraction would be: 2 2/6 or reduced to 2 1/3
She used 2 1/3 yards of fabric.
The question asks for how much she has left so, we must subtract 2 1/3 from 3 1/2
However, we must have a common denominator to subtract.
To find this, we can list the multiples of both of the denominators:
2: 2,4,6,8,10
3: 3,6,9,12,15
The LCM (Lowest Common Denominator) is 6.
2*3=6
3*2=6
We must do the same for the numerator as what is done for one-half has to be done for the other.
1*3=3
1*2=2
The New fractions would be:
3 3/6
and
2 2/6
Now we can subtract ;
3-2=1
3-2=1
We don't subtract the denominator
The answer is 1 1/6.
Erica would have 1 1/6 of the curtain left.
Hope this Helps!
-Benjamin :)
Consider △LNM. Which statements are true for triangle LNM? Check all that apply. The side opposite ∠L is NM. The side opposite ∠N is ML. The hypotenuse is NM. The hypotenuse is LN. The side adjacent ∠L is NM. The side adjacent ∠N is ML.
Answers
According the diagram given the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.
Given :
Triangle LNM.
Acccording to the given triangle (attached below):
The base of the triangle LNM is LM.The perpendicular of the triangle LMN is NM.The hypotenuse of the triangle LMN is LN.The opposite side of [tex]\rm \angle L[/tex] is MN.The opposite side of [tex]\rm \angle N[/tex] is LM.Therefore, the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.
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In triangle LNM, the side opposite angle L is NM, and the side opposite angle N is ML. The side adjacent to angle L is NM, and the side adjacent to angle N is ML. The hypotenuse of triangle LNM is LN, not NM.
Explanation:In triangle LNM, the side opposite angle L is NM, so the statement "The side opposite ∠L is NM" is true.
In triangle LNM, the side opposite angle N is ML, so the statement "The side opposite ∠N is ML" is true.
The hypotenuse of triangle LNM is LN, not NM, so the statement "The hypotenuse is NM" is false.
The side adjacent to angle L is NM, so the statement "The side adjacent ∠L is NM" is true.
The side adjacent to angle N is ML, so the statement "The side adjacent ∠N is ML" is true.
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Water weighs about 8.34 pounds per gallon. About how many ounces per gallon is the weight of water?
Answers
the weight of the water is 133.44 oz per gallon
Would you measure walls using inches or yards
Answers
an ellipse has a center at the origin, a vertex along the major axis at (13, 0), and a focus at (12, 0). What is the equation of the ellipse?
Answers
Answer: The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
Step-by-step explanation: We are given to find the equation of an ellipse that has a center at the origin, a vertex along the major axis at (13, 0) and a focus at (12, 0).
Since the focus lies on the X-axis, so the standard equation of an ellipse with major axis as X-axis is given by
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
According to given information, we have
a vertex along the major axis, (a, 0) = (13, 0)
⇒ length of the major axis, a = 13,
co-ordinates of focus, (c, 0) = (12, 0)
⇒ c = 12.
We know that
[tex]c^2=a^2-b^2.[/tex]
Therefore,
[tex]12^2=13^2-b^2\\\\\Rightarrow 144=169-b^2\\\\\Rightarrow b^2=169-144\\\\\Rightarrow b^2=25\\\\\Rightarrow b=5.[/tex]
Thus, from equation (i), we get
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\\\Rightarrow \dfrac{x^2}{13^2}+\dfrac{y^2}{5^2}=1\\\\\\\Rightarrow \dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse along the major axis at (13, 0), and a focus at (12, 0) is; x²/169 + y²/25 = 1
Equation of an ellipseThe equation of an ellipse whose center is the origin, (0,0) usually takes the form;
x²/a² + y²/b² = 1The coordinates of the vertex on the major axis is given as; (13,0) and the focus at (12,0)
Hence, the square of the length of the minor axis;
b² = a² - c²b² = 169 - 144b² = 25.Hence, the equation of the described ellipse is;
x²/169 + y²/25 = 1Read more on equation of an ellipse;
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The directions for mixing an insect spray say to use 1 3/4 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 4 1/5 gallons of water?
Answers
Now convert the new water gallons to an improper fraction: 4 1/5 gallons
--> 21/5 gallons
Now 21/5 gallons water × 7/3oz./gallon water = 21×7/5×3 = 7×7/5 = 49/5oz.--> convert to mixed number: 9 4/5oz. chemical in order to make 4 1/5 gallons of mixture.
7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
To determine the amount of chemical to mix with 4 1/5 gallons of water, you need to use the given ratio of 1 3/4 ounces of chemical per gallon of water.
1.) Convert 4 1/5 gallons to a mixed number:
4 1/5 = 21/5 gallons.
2.) Multiply the amount of water by the chemical-to-water ratio:
(21/5) gallons * (7/4) ounces = 147/20 ounces.
3.) Convert 147/20 ounces to a mixed number:
147/20 = 7 7/20 ounces.
Therefore, 7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
A rectangle field with area 300 square meters has a length that is 5 meters more than it's width. If W represents the width of the field then an equation that can be used to determine the value of W is?
A) w^2-1500
B) w^2-295
C) w^2+5w-300
D) w^2-5w-300
E) 5w^2-300
Answers
The equation that would be used to determine the value of w is expressed as: C. w² + 5w - 300
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the following:
Area = 300 sq. mWidth = wLength = (w + 5) mTherefore, equation that would be used to find the value of w is:
(w + 5)(w) = 300
w² + 5w = 300
w² + 5w - 300
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a car is traveling at a rate of of 55 miles per hour. how many feet oer hour does the car travel?
Answers
A building 64 ft high casts a 288-ft shadow. Sarah casts a 18-ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?
Answers
s=1152/288
s=4 ft
So Sarah is four feet tall.
Please Help ASAP
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) =x^2-320x+40,052 . What is the minimum unit cost? Do not round your answer.
Answers
the lowest point, or lowest cost value, it reaches, is the U-turn point, or vertex
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ 1}}x^2&{{ -320}}x&{{ +40052}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so, the lowest cost is at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]
Find the amount of time to the nearest day it would take a deposit of $1300 to grow to 1 million at 17% compounded continuously. The amount of time it would take to grow the deposit to $1 million is____ years ___ days
Answers
[tex]\bf 1000000=1300e^{0.17t}\implies \cfrac{1000000}{1300}=e^{0.17t}\implies \cfrac{10000}{13}=e^{0.17t} \\\\\\ ln\left( \frac{1000000}{1300} \right)=ln(e^{0.17t})\implies ln\left( \frac{1000000}{1300} \right)=0.17t \\\\\\ \cfrac{ln\left( \frac{1000000}{1300} \right)}{0.17}=t\impliedby years[/tex]
now, how many days? simply multiply t * 365.
It would take approximately 39 years and 183 days for the deposit to grow to $1 million.
Use the concept of compound interest defined as:
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given that,
Initial deposit: $1300
Target amount: $1 million
Interest rate: 17%
Compounding: Continuous
Time to calculate: To the nearest day
To find the amount of time it would take,
Use the formula:
[tex]t = \dfrac{ln(\frac{M}{P})}{r}[/tex]
Where,
t = time in years
M = final amount ($1 million)
P = initial deposit ($1300)
r = interest rate (17% or 0.17)
Find the natural logarithm of the ratio M/P:
ln(1,000,000 / 1,300) ≈ 6.64
Divide the result by the interest rate:
t = 6.64 / 0.17
t ≈ 39.05 years
So, it would take approximately 39 years to grow the deposit to $1 million.
To determine the number of days,
Multiply the decimal part of the years by 365 (assuming a non-leap year):
0.05 x 365 ≈ 183 days
Hence,
Rounding to the nearest day, it would take approximately 39 years and 183 days for the deposit to grow to $1 million.
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1) Which number rounds up when rounded to the nearest tenth?
55. 24
170.93
0.12
8.15
___________
2)
Estimate the value of 2968 + 9912 by rounding each number to the thousands.
14,000
13,000
12,000
7000
___________
3)
Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4
25 times 4 = 100
30 times 5 = 150
27 times 4 = 108
20 times 4 = 80
_____________
4)
Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.
30
33
123
130
___________
5)
Determine which answer is reasonable for 4. 8 times 9.2.
14
45.36
432
870.4
(please be 100 sure)
Answers
170.93
8.15
you are looking at the hundreds place to decided if one runs up or not. 5 or higher rounds up, 4 to zero stays the same
#2: 2913 = 3000; 9912 = 10000
10000 + 3000 = 13000
B.13000
#3: 27 x 4 = 108
if 'friendly' means making it easier, like 27 becomes 30 and 4 becomes 5, well idk what friendlier means so... i give you the exact number. But it looks like 30 x 5 if that is what friendlier means
#4: 78 + 45 = 80 + 50 (round it up)
80 + 50 = 130
D) 130
#5 4.8 x 9.2 = 44.16
closest is 45.36 so...
B) 45.36
hope this helps
f(x) = 2/3 x -5 what is the value f(6)?
Answers
f(6)=4-5
f(6)=-1
Final answer: f(6)= -1
Makers Corp. had additions to retained earnings for the year just ended of $395,000. The firm paid out $195,000 in cash dividends, and it has ending total equity of $5.3 million. What is the net income?
Answers
Net income=395,000+195,000
Net income=590,000
write a formula for the nth term of the sequence. Identify your formula as recursive or explicit. -3,3,-3,3,-3,3
Answers
a sub n= -1*a sub n-1
recursive
what is the least common multiple of 20 and 52
Answers
hope this helps:)
The least common multiple of 20 and 52 is, 420
What is Least common multiple?The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 20 and 52
Now, The factors of numbers are,
⇒ 20 = 2 × 2 × 5
⇒ 42 = 2 × 3 × 7
Hence, The least common multiple of 20 and 52 is,
⇒ LCM of {20, 52} = 2 × 2 × 5 × 3 × 7
= 420
Thus, The least common multiple of 20 and 52 is, 420
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vito just put some money into a cd that pays 12.7 interest compound quarterly. according to the rule of 72,in the approximately how years will he have 4 times the amount of money that he has now
Answers
Answer:
11.34 years.
Step-by-step explanation:
We have been Vito put some money into a cd that pays 12.7 interest compound quarterly.
Since the rule of 72 states that to find the number of years it will take an amount to double, we need to divide 72 by annual interest rate.
First of all let us find the number of years it will take to double Vito's money by dividing 72 by 12.7.
[tex]\text{Time it will take to double Vito's money}=\frac{72}{12.7}[/tex]
[tex]\text{Time it will take to double Vito's money}=5.66929133858\approx 5.669[/tex]
Since it will take 5.669 years to double Vito's money, so to find the time it will take Vito to have 4 times the money, we will multiply 5.669 by 2.
[tex]\text{Time it will take to have 4 times Vito's money}=5.669*2[/tex]
[tex]\text{Time it will take to have 4 times Vito's money}=11.338\approx 11.34[/tex]
Therefore, approximately in 11.34 years Vito will have 4 times the amount of money that he has now.
A tree is 6 feet 4 inches tall. How tall is it in inches?
Answers
The number of inches in 6 feet 4 inches tall is 76 inches.
Given that, a tree is 6 feet 4 inches tall.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 feet = 12 inches
So, 6 feet = 6×12
= 72 inches
Now, in inches = 72+4
= 76 inches
Therefore, the number of inches in 6 feet 4 inches tall is 76 inches.
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the slope of a line is 2/3. what is the slope of a line that is perpendicular to this line? Type a numerical answer in the space provided. do not include spaces in your answer. if necessary, use the / key to represent a fraction bar and only type improper fractions (no mixed numbers).
Answers
Which is a better deal on a $39.99 item: 50% off original price or 40% off, plus additional 20% at the register?
Answers
Hope this helps****; )