Answer:
the percentage of people who have an IQ between 115 and 140 is 16.79%
Step-by-step explanation:
From the information given:
We are to determine the percentage of people who have an IQ between 115 and 140.
i.e
P(115 < X < 140) = P( X ≤ 140) - P( X ≤ 115)
[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]
From Z tables :
[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]
[tex]P(115 < X < 140) = 0.1679[/tex]
Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%
Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 100[/tex].The standard deviation is of [tex]\sigma = 15[/tex].The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 100}{16}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
X = 115:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{16}[/tex]
[tex]Z = -0.94[/tex]
[tex]Z = -0.94[/tex] has a p-value of 0.1736.
0.9938 - 0.1736 = 0.8202.
0.8202 = 82.02% of people who have an IQ between 115 and 140.
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Tubby Toys estimates that its new line of rubber ducks will generate sales of $7 million, operating costs of $4 million, and a depreciation expense of $1 million. If the tax rate is 25%, what is the firm’s operating cash flow?
Answer:
2.5m
Step-by-step explanation:
Using the adjusted accounting profits method.
Operating cash flow = After - tax profit + Depreciation. .......... ( 1 )
Given that :
* depreciation expense = $1 million
* Sales generated $7 million
* Tax rate = 25%
Tax rate = 25/100
= 0.25
From equation 1
= ( 7m - 4m - 1m ) ×( 1 - 0.25 ). + 1m
= ( 7m - 5m ) × ( 0.75 ) + 1m
= 2m × 0.75 + 1m
= 1.5m + 1m
= 2.5m
The firm operating cash flow = 2.5m
which of the following graph represents the solution set for the inequality 3 - 1/2 x > 10
Answer:
56
Step-by-step explanation:
A toy falls from a window 70 feet above the ground. How long does it take the toy to hit the ground?
Answer:
2.09 seconds.
Step-by-step explanation:
We are given...
y = 70 feet
v0 = 0 feet/second
a = 32 feet/second^2
We need to find t using the following equation...
y = v0 * t + (1/2) * a * t^2
70 = 0 * t + (1/2) * 32 * t^2
70 = (1/2) * 32 * t^2
70 = 16t^2
16t^2 = 70
t^2 = 4.375
t = sqrt(4.375)
t = 2.091650066
So, it will take the toy about 2.09 seconds to hit the ground.
Hope this helps!
What is the scale factor of ABC to DEF?
Answer:
B.3
Step-by-step explanation:
to get the scale factor divide a side from the bigger triangle by the equivalent in the small one
15/5 = 3
see attached the question is in an image attached
37.62202 sq units
First, calculate the areas of the separate triangles:
ABD = 20.19968 sq units
ACD = 17.46234 sq units
then add them to get 37.62202 sq units
Answer:
30.51 units^2
Step-by-step explanation:
Well to find the area of a triangle without height we use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
To find S we use the following formula,
[tex]S = \frac{1}{2} (a+b+c)[/tex]
So a b and c are the sides of a triangle, we'll start with the left triangle.
S = 1/2(7 + 5.22 + 7.4)
S = 1/2(19.62)
S = 9.81
Now we can plug in 9.81 for S,
[tex]A = \sqrt{9.81(9.81-a)(9.81-b)(9.81-c)}[/tex]
[tex]A = \sqrt{9.81(9.81-7)(9.81-5.22)(9.81-7.4)}[/tex]
[tex]A = \sqrt{9.81(2.81)(4.59)(2.41)}[/tex]
[tex]A = \sqrt{9.81(31.083939)}[/tex]
[tex]A = \sqrt{304.93344159}[/tex]
[tex]A = 17.46234353086664[/tex]
But we can just simplify that to the nearest hundredth place which is,
17.46.
Now for the next triangle,
[tex]S = \frac{1}{2} (6.36 + 6.85 + 7.4)[/tex]
[tex]S = \frac{1}{2} (20.61)[/tex]
[tex]S = 10.305[/tex]
Plug in 10.305 for S,
[tex]A = \sqrt{10.305(10.305-6.36)(10.305-6.85)(10.305-7.4)}[/tex]
[tex]A = \sqrt{10.305(3.945)(3.455)(2.905)}[/tex]
[tex]A = \sqrt{10.305(16.534975)}[/tex]
[tex]A = \sqrt{170.392917375}[/tex]
A = 13.053463807549
We can round it to the nearest hundredth,
A = 13.05
So we just add 17.46 + 13.05
= 30.51 units^2
Thus,
the area of the figure is 30.51 units^2.
Hope this helps :)
A square based brass plate in 4mm high and has a mass of 1.05kg. The density of the brass is 4.2g/cm3, calculate the length of the plate in centimeters
Answer:
[tex]Length = 25cm[/tex]
Step-by-step explanation:
Given
Brass Shape: Square
[tex]Density = 4.2g/cm^3[/tex]
[tex]Mass = 1.05kg[/tex]
[tex]Height = 4mm[/tex]
Required
Determine the length of the plate
First, we need to calculate the Volume of the Brass using
[tex]Density = \frac{Mass}{Volume}[/tex]
Make Volume the subject of formula
[tex]Volume = \frac{Mass}{Density}[/tex]
Substitute 1.05kg for Mass and 4.2g/cm³ for Density
[tex]Volume = \frac{1,05\ kg}{4.2\ g/cm^3}[/tex]
Convert 1.05 kg to grams
[tex]Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = 250cm^3[/tex]
Next is to determine the Area of the brass;
[tex]Volume = Height * Area[/tex]
Substitute 250cm³ for Volume and 4mm for Height
[tex]250cm^3 = 4mm * Area[/tex]
Convert mm to cm
[tex]250cm^3 = 4 * 0.1cm * Area[/tex]
[tex]250cm^3 = 0.4cm * Area[/tex]
Divide both sides by 0.4cm
[tex]\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}[/tex]
[tex]\frac{250cm^3}{0.4cm} =Area[/tex]
[tex]625cm^2 = Area[/tex]
[tex]Area = 625cm^2[/tex]
Lastly, we'll calculate the length of the brass
Since the brass is square based;
[tex]Area = Length^2[/tex]
Substitute 625cm² for Area
[tex]625cm^2 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{625cm^2} = Length[/tex]
[tex]25cm = Length[/tex]
[tex]Length = 25cm[/tex]
Hence, the length of the square brass is 25cm
Identify the parameter n in the following binomial distribution scenario. A basketball player has a 0.479 probability of
making a free throw and a 0.521 probability of missing. If the player shoots 17 free throws, we want to know the probability
that he makes more than 9 of them. (Consider made free throws as successes in the binomial distribution.)
Answer:
n = 17
Step-by-step explanation:
Assuming
- probability of success (making free throw) does not vary
We have
n = 17 (trials)
p = 0.479
x > 9
The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"
[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]
Know we calculating the P(makes more than 9 of them)
[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]
Using the R-code:
[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]
Learn more:
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the endpoints of GH are g(-7,3) and h(1,-2) what’s the midpoint of GH
Answer: [tex]\bigg(-3,\dfrac{1}{2}\bigg)[/tex]
Step-by-step explanation:
G = (-7, 3) H = (1, -2)
[tex]M_{GH}=\bigg(\dfrac{X_G+X_H}{2},\dfrac{Y_G+Y_H}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-7+1}{2},\dfrac{3+(-2)}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-6}{2},\dfrac{1}{2}\bigg)\\\\\\.\qquad = \large\boxed{\bigg(-3,\dfrac{1}{2}\bigg)}[/tex]
The mid point of the line GH whose end points are (-7,3) and (1,-2) is (-3,1/2).
What is the mid point of a line?The mid point is a line which divides the line into two equal parts. The formula to calculate the mid point of line whose end points are (x1,y1) and (x2,y2) is {(x1+x2)/2,(y1+y2)/2}.
How to calculate mid point of a line?To calculate the mid point of the line GH we have to put x1=-7, x2=1,y1=3 and y2=-2 so,
the mid point is {(-7+1)/2,(3-2)/2}
=(-3,1/2)
Hence the mid points of a line GH whose end points are g(-7,3) and h(1,-2) is (-3/1/2).
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Enter the correct answer in the box by replacing the values of a and b. f(x) = a(b)^x
Answer:
f(x)= 8(0.5)^x
Step-by-step explanation:
As you can see on the graph there are two specific points labeled:
(0,8) and (1,4)
The 8 would be the initial value and starting point of the "design"
A is always the initial value so replace that.
Then proceed to divide 4 by 8 to figure out the percentage change its 0.5
leave x as it is
Find the approximate sum of the series shown below.
Answer:
its D
Step-by-step explanation:
The approximate sum is 134.83
The correct option is (D).
What is series?
A series in math is simply the sum of the various numbers or elements of the sequence.
For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5 we will simply add them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
A series in math is the sum of the terms in a sequence. The series and the sequence given in this example are almost identical. What differentiates the two is the addition of the + sign. Changing the comma to a plus sign changes the sequence into a series.
Suppose a person wanted to increase their level of fitness. The person decides to walk for 15 minutes the first day and increases the time spent walking by 5 minutes each day for the first week. The sequence that shows this example is
15, 20, 25, 30, 35, 40, 45
series used to find the answer is
15+20+25+30+35+40+45
Given:
[tex]\sum[/tex] (k =1 to 8) 5* (4/3)^(k-1)
So,
Putting values k=1 to 8 one by one then
= 5 + 20/3 + 80/9+0320/27+......+81920/2187
=294875/2187
=134.83
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What is the value of x in the diagram below?
A.
6
B.
4
C.
5
D.
3
Answer:
[tex]\boxed{3}[/tex]
Step-by-step explanation:
We can use ratios to solve since the sides are proportional.
[tex]\frac{18}{x} =\frac{48}{8}[/tex]
Cross multiply.
[tex]48x=18 \times 8[/tex]
Divide both sides by 48.
[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]
[tex]x=3[/tex]
The value of x in the given triangle is 3.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given are two similar triangles,
Therefore, they have the same ratio of corresponding sides
18/48 = x/8
x = 3
Hence, The value of x in the given triangle is 3.
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Constructing a cube with double the volume of another cube using only a straightedge and compass was proven possible by advanced algebra.
True or False?
Answer:
False
Step-by-step explanation:
It was proved with advanced algebra that a doubled cube could never be constructed with a straightedge and compass
x(x+3)(x+3)=0 Please I NEED HELP FAST! PLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
Answer:
[tex]\boxed{x^3+6x^2+9x}[/tex]
Step-by-step explanation:
[tex]x(x+3)(x+3)[/tex]
Resolving the first parenthesis
[tex](x^2+3x) (x+3)[/tex]
Using FOIL
[tex]x^3+3x^2+3x^2+9x[/tex]
Adding like terms
[tex]x^3+6x^2+9x[/tex]
[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]
[tex]x(x+3)(x+3) =0[/tex]
[tex]\boxed{x_1 =0}[/tex]
[tex]x_2+3 =0[/tex]
[tex]\boxed{x_2 = -3}[/tex]
[tex]x_3+3 =0[/tex]
[tex]\boxed{x_3 = -3}[/tex]
The mean of normally distributed test scores is 82 and the standard deviation is 5. If there are 241 test scores in the data sample, how many of them were in the 92 to 97 range?
Answer:
5
Step-by-step explanation:
Find the z-scores.
z = (x − μ) / σ
z₁ = (92 − 82) / 5
z₁ = 2
z₁ = (97 − 82) / 5
z₂ = 3
Find the probability:
P(92 < X < 97)
P(2 < Z < 3)
P(Z < 3) − P(Z < 2)
0.9987 − 0.9772
0.0215
Find the number of tests:
0.0215 (241) ≈ 5
Please help with this
Answer: B
Step-by-step explanation:
Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.
Hope it helps <3
What would be the Excel Formula to solve this question?
Deb and Rusty know that buying a house will save them money on taxes because they get to deduct the interest they pay to the bank each year and the property taxes they pay each year. First create a separate worksheet from the amortization schedule. Title this worksheet Analysis. In this worksheet, create a column titled Income starting at $90,000 and increasing at 3% for 20 years. What is their income after 20 years?
Answer:
Income after 20 years = 162550.01
Step-by-step explanation:
In cell B2, enter 90000
In cell B3, enter +B2*1.03
Copy cell B3 to cells B4:B22
Set number format for column B to 2 decimal places.
Read cell B22 = 162550.01
Income after 20 years = 162550.01
Their income after 20 years would be; 72,550 dollars.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
The income after 20 years can easily be determine by using compounding
Thus the formula;
Future Value = Present Value (1 + I)^ 20
= 90,000 (1 + 0.03)^ 20
= 162,550 dollars
Income can be determing by subtracting Pv from Fv i.e
Income = 162,550 - 90,000 = 72,550
Calculation on excel sheet;
A B C D
1 90,000 1.03 = A1 x1.03 = C1-A1
2 = D1 1.03 = A2 x 1.03 = C2-A2
20 = D19 1.03 = A20 x 1.03 = A20 - C20
Thus, In work sheet colunm D will show the income on investment.
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Part F
I NEED HELP!
What is the geometric mean of the measures of the line segments A Dand DC? Show your work.
Answer:
AC2 = AB2 + BC2 ---> AC2 = 122 + 52 ---> AC = 13
AD / AB = AB / AC ---> AD / 12 = 12 / 13 ---> AD = 144/13
DC = AC - AD ---> DC = 13 - 144/13 ---> DC = 25/13
AD / DB = DB / DC ---> DB2 = AD · DC ---> DB2 = (144/13) · (25/13) ---> DB = 60/13
DB is the geometric mean of AD and DC.
Step-by-step explanation:
43.
Some of the ingredients used by a baker for making 1 dozen
normal sponge cakes are listed below:
225g unsalted butter; 4 eggs; 125ml milk;
2 tsp vanilla extract; 264g plain flour
To make fully vegetarian cakes, the baker replaces each egg
with an additional 30g of plain flour.
The baker got an order for 100 normal cakes and 60 vegetarian
cakes. How much kilograms of flour would the baker need to
complete the order?
Answer:
4.12 kg
Step-by-step explanation:
Regular cakes:
1 dozen normal sponge cakes: 264 g plain flour
Vegetarian cakes:
1 dozen cakes: 264 g plain flour
4 eggs are replaced by 4 * 30 g of flour = 120 g flour
total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g
Proportion for regular cakes:
12 cakes to 264 g flour = 100 cakes to x grams flour
12/264 = 100/x
12x = 26400
x = 2200
2200 g flour for 100 regular cakes
Proportion for vegetarian cakes:
12 cakes to 384 g flour = 60 cakes to y grams flour
12/384 = 60/y
12y = 384 * 60
12y = 23040
y = 1920
1920 g flour for 60 vegetarian cakes
Total flour needed:
2200 g + 1920 g = 4120 g
4120 g * 1 kg/(1000 g) = 4.12 kg
Answer: 4.12 kg
Find the balance in Asturos savings account if he deposits $2100 at 3.5% simple interest for 2 years
Answer:
2250
Step-by-step explanation:
Balance : 2100
2 Years
2100 ÷ 100 x 103.5 ÷ 100 x 103.5 = 2249.5725
a rope is wound 50 times around a cylinder of radius 25cm. How long is the rope
Circumference of the cylinder :
C = 2 x pi x r
C = 2 x 3.14 x 25 = 157 cm
Multiply the circumference by number of wraps:
157 x 50 = 7,850 cm long ( 78.5 meters)
Tessellations that use more than one one type of regular polygon are called regular tessellations?
Answer:
False
Step-by-step explanation:
A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.
helPpppPPppPPPppppPppppPPppppppPPPPPPPPpppppppPPPPpppppppPPPPppppppPPPPppppppPPPPPpppppPPPPPPPPPPPPPPPPPPppppPPPPPPPppppPPPpppppPPpp THANK YOU
Answer:
1) rectangle
2) rectangle
Step-by-step explanation:
Any cross section of a rectangular prism is a rectangle.
Hope it helps <3
PLEASE I NEED HELP!!! FIRST ANSWER GETS BRAINLIEST!!!
Reduce to Simplest form. -5/8+(-8/5)
Answer:
[tex]\frac{-89}{40}[/tex]
As a Proper Fraction: -2[tex]\frac{9}{40}[/tex]
Step-by-step explanation:
So i assume the fraction sits like this:
[tex]\frac{-5}{8}[/tex] + [tex]\frac{-8}{5}[/tex]
This essentially becomes:
[tex]\frac{-5}{8}[/tex] - [tex]\frac{8}{5}[/tex]
Now multiply the denominators for a LCM (Lowest common denominator)
8*5 = 40
And now multiply the top parts with the respective denominator (-5 * 5) and (8 * 8)
So Now you get
[tex]\frac{-25}{40}[/tex] - [tex]\frac{64}{40}[/tex]
and now that u have same denominators, just subtract -25 - 64 and get -89
Final Simplified answer: [tex]\frac{-89}{40}[/tex]
As a Proper Fraction: -2[tex]\frac{9}{40}[/tex]
Find the area of the trapezoid in the figure below round your final answer to the nearest tenth
Answer: 60.9 u^2
Step-by-step explanation:
The area of a trapezoid can be calculated as seen in the attachment.
Thus:
[tex]A = \frac{3.7+14.2}{2} * 6.8\\A = \frac{17.9}{2} *6.8\\A = 8.95*6.8\\A = 60.86\\Round\\\left[\begin{array}{c}A=60.9\end{array}\right][/tex]
Hope it helps <3
Answer:
60.9 units^2
Step-by-step explanation:
Well the formula for the area of a trapezoid is,
[tex]\frac{b1+b2}{2} h[/tex]
So b1 and b2 are 142 and 3.7,
14.2 + 3.7 = 17.9
17.9 ÷ 2 = 8.95
8.95 × 6.8 = 60.86
60.9 units^2 rounded to the nearest tenth.
Thus,
the area of the trapezoid is 60.9 units^2.
Hope this helps :)
Determine which type of correlation is shown in the graphed relationship
Answer:
No correlation
Step-by-step explanation:
Hey there! :)
This has no correlation because all the points are spread out throughout the graph making no correlation.
Answer:
D no correlation
Step-by-step explanation:
too many scattered dot all over the place if its some going up down its NO CORRELATION!!!
I really need help on this question
Answer:
d. 38
Step-by-step explanation:
AB = AD - BD = 54 - 36 = 18
AC = AB + BC = 18 + 20 = 38
How much would a computer system cost if you pay $200 down and made 12 monthly payments of only $98.95?
Answer:
$1387.4
Step-by-step explanation:
Total cost for the computer will be sum of down payments and monthly installments.
____________________________________
Given
down payment = $200
monthly installment value = $98.85
no. of installments = 12
total value of monthly installments = 12*98.95 = $1187.4
Total cost of computer system = $200+ $1187.4 = $1387.4
x/3 ≥−33 solve for x answer must be simplified
Answer:
[tex]\boxed{x\geq -99}[/tex]
Step-by-step explanation:
[tex]\frac{x}{3} \geq -33[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 3.[/tex]
[tex]\frac{x}{3} (3) \geq -33(3)[/tex]
[tex]x\geq -99[/tex]
Answer:
[tex]\boxed{\red{x \geqslant - 99}}[/tex]
Step-by-step explanation:
[tex] \frac{x}{3} \geqslant - 33 \\ x \geqslant - 33 \times 3 \\ x \geqslant - 99[/tex]
hope this helps you!
Why should you find the least common denominator when adding or subtracting rational expressions?
Answer:
It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.
Step-by-step explanation:
for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0.0143. (a) What is the probability that the distance is at most 100 m? What is the probability that the distance is at most 200 m? What is the probability that the distance is between 100 m and 200 m? (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (c) What is the value of the median distance?
Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.[tex]e^{-\lambda.x}[/tex]
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 - [tex]e^{-\lambda.x}[/tex]
(a) Probability of distance at most 100m, with λ = 0.0143:
F(100) = 1 - [tex]e^{-0.0143.100}[/tex]
F(100) = 0.76
Probability of distance at most 200:
F(200) = 1 - [tex]e^{-0.0143.200}[/tex]
F(200) = 0.94
Probability of distance between 100 and 200:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) = [tex]\frac{1}{\lambda}[/tex]
E(X) = [tex]\frac{1}{0.0143}[/tex]
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ = [tex]\sqrt{\frac{1}{\lambda^{2}} }[/tex]
σ = [tex]\sqrt{\frac{1}{0.0143^{2}} }[/tex]
σ = 69.93
Distance exceeds the mean distance by more than 2σ:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - [tex]e^{-0.0143*209.79}[/tex])
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
[tex]\int\limits^m_0 f({x}) \, dx[/tex] = 0.5
[tex]\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx[/tex] = 0.5
[tex]\lambda.\frac{e^{-\lambda.x}}{-\lambda}[/tex] = [tex]-e^{-\lambda.x} + e^{0}[/tex]
[tex]1 - e^{-\lambda.m}[/tex] = 0.5
[tex]-e^{-\lambda.m}[/tex] = - 0.5
ln([tex]e^{-0.0143.m}[/tex]) = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46