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
Compare the following two sets of data by using box-and-whisker plots. Explain the similarities and differences between the two data sets. Set A = {56, 62, 71, 82, 92, 101, 106, 103, 97, 84, 68, 57} Set B = {36, 42, 48, 56, 63, 72, 78, 75, 69, 58, 46, 37}
Answer:
After graphing you can see that There are many differences between the sets. In general for A, values are much higher, the mean median for the set A is above 80 whereas the median for B is below 60, the maximum of A is above 100 and the maximum for B is about 80.
Step-by-step explanation:
With python you can use this code to see the graph.
import pandas as pd
import seaborn as sns
dfA = pd.DataFrame()
dfB = pd.DataFrame()
dfA['Value'] = pd.Series([56, 62, 71, 82, 92, 101, 106, 103, 97, 84, 68, 57])
dfA['Letter'] = 'A'
dfB['Value'] = pd.Series([36, 42, 48, 56, 63, 72, 78, 75, 69, 58, 46, 37])
dfB['Letter'] = 'B'
df = pd.concat([dfA,dfB],axis = 0).reset_index(drop = True)
sns.boxplot(x = 'Letter', y = 'Value', data = df)
After graphing you can see that There are many differences between the sets. In general for A, values are much higher, the mean median for the set A is above 80 whereas the median for B is below 60, the maximum of A is above 100 and the maximum for B is about 80.
Answer:
A values are higher, above 80 and max 100.
B values are lower than 60 and max 80.
From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?
Answer:
12100
Step-by-step explanation:
If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985
In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990
The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;
B ( t ) = − 329.4 t + 13747
B(5) = -329.4(5) + 13747
B(5) = -1647+13747
B(5) = 12100
This shows that there will be 12100 federally insured banks are there in the year 1990.
Find the zeros of g(x) = x3 + x2 – 9x – 9
Answer: The zeros are -1,-3, and 3
Hope this helps
Answer:
let g[x]=0
then0=x3−x2-9x+9
rewrite it as x3−x2−9x+9=0
by factorising it becomes
(x−1)(x+3)(x−3)=0
therefore
either x-1=0 OR x+3=0 OR x-3=0
which becomes
x=1 OR x=-ve3 OR x=3
are the zeroes of the polynomial
hope this helps
help me plz I really dont get it
Suppose we want to choose 5 letters, without replacement, from 10 distinct letters. How many ways can this be done, if the order of the choices is relevant? How many ways can this be done, if the order of the choices is not relevant?
Step-by-step explanation:
If the order is relevant, the number of permutations is:
₁₀P₅ = 30,240
If the order is not relevant, the number of combinations is:
₁₀C₅ = 252
The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240.
What are permutation and combination?When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
The number of ways to choose r quantity among n without replacement is given as nCr = n!/(r!(n - 1)!)
n = 10 and r = 5
10C5 = 252
The number of ways to choose r quantity among n with replacement is given as, nPr = n!/(n - r)!
n = 40 and r = 5
10P5 = 10!/(10 - 5)! = 30240
Hence "The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240".
For more about permutation and combination,
https://brainly.com/question/13387529
#SPJ2
A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of
the cardboard in inches?
Area = 36 - square inches
4
width = 4 inches
length = ?
8 7 7
Og
11
O 32
20
O 154
7
20
Answer:
9 inchesStep-by-step explanation:
Area of the rectangular cardboard = Length * Width ... 1
Given the area of the cardboard = 36-square inches
If the length of the cardboard can be found by dividing its area by its width, then Length = Area/Width ... 2
Given the width to be 4 inches
Length = 36 in²/4 in
Length of the cardboard = 9 inches
Which is the equation of the line for the points in the given table
Answer:
A...............................
E={a,c,f}
A={a,c,j}
find the intersection of E and A.
find the union of E and A
write your answer using set notation (in roster form)
Answer:
i. E ∩ A = { a , c }ii. E ∪ A = { a , c , f , j }Step-by-step explanation:
Given
E = { a , c , f }
A = { a , c , j }
i) Let's find the intersection of E and A
E ∩ A = { a , c , f } ∩ { a , c , j }
In the case of intersection , we have to list the elements which are common in both sets:
E ∩ A = { a , c }
ii) Let's find the union of E and A
E ∪ A = ( a , c , f } { a , c , j }
In the case of Union, we have to list all the elements which are present in both sets.
E ∪ A = { a , c , f , j }
Hope this helps..
Best regards!!
expand (x+2y)^2 plzzzzzzzz
g Given p, q, and r three propositional variables, how many different ways are for the propositional logic formula (p -> q) ^ (q -> r) ^ p to be evaluated to FALSE
Answer:
There are 7 ways in which the formula can be evaluated to False.
Step-by-step explanation:
In order to solve this problem we will need to build a truth table. In order to build the truth table, we must start by setting the possible truth values combinations. In total there must be 8 rows, which you can see on the first three columns of the attached table.
Next, it is advisable that you divide the formula in little chunks of information that will be easier to evaluate. One column can be (p->q).
Let's evaluate that first column. In general, that column can only be false if p=T -> q=F. Which happens only on the 3dr and 4th rows of the table. The rest of the statements are true.
The next column will be (q->r). The same condition is met here, but this time you take into account the values given on the q and r columns. The false values will happen only on the 2nd and 6th rows. The rest of the rows for that collumn should be true.
Finally you can test for the whole formula. the first, 4th and 5th columns must be true for the formula to be true as well, which will happen only on the first row. The rest of the rows will have at least one false statement which makes the whole row false. So the rest of the rows are false.
(see attached picture for the whole truth table)
10 points + brainliest... IF you can tell me if I'm right or wrong! (no explanation needed but the person with most explanation will get brianleist)
Answer:
All correct
Step-by-step explanation:
All proposed answers correct, and well indicated in set notation.
(6/22 + 5/77) ^2 equalviant to in fraction form
Answer:
676/5929
Step-by-step explanation:
8mi 200 yds - 2 mi 528 yds =
Answer:
5 mi 1432 yds
Step-by-step explanation:
8mi 200 yds
- 2 mi 528 yds
---------------------------
We have to borrow 1 mile and convert to yards
1 mile = 1760 yds
7mi 200+1760 yds
- 2 mi 528 yds
---------------------------
7mi 1960 yds
- 2 mi 528 yds
---------------------------
5 mi 1432 yds
Answer:
8mi 200yds - 2mi 528yds
= 5mi 1432yds
Step-by-step explanation:
1 mile = 1760 yards
8 miles = 7miles + 1 mile = 7 miles + 1760 miles = 7 miles 1760 yards
8miles 200 yards = 7miles + 1760 yards + 200 yards = 7miles + 1960 yards
then:
8mi 200 yds - 2 mi 528 yds = 7mi 1960yds - 2mi 528yds
7mi 1960yds
- 2mi 528yds
= 5mi 1432yds
Jenna drives on average 46 miles per day with a standard deviation of 5.3 miles per day. Suppose Jenna's miles driven per day are normally distributed. Let X = the number of miles driven in a given day. Then X - N(46, 5.3). If necessary, round to three decimal places.
Provide your answer below:
Suppose Jenna drives 41 miles on Monday. The Z-score when x - 41 is______ . The mean is________ This z-score tells you that x = 41 is________ standard deviations to the left of the mean.
Answer:
Suppose Jenna drives 41 miles on Monday. The Z-score when x - 41 is [tex]-0.943[/tex]. The mean is [tex]46[/tex] This z-score tells you that x = 41 is [tex]0.94[/tex] standard deviations to the left of the mean.
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 46\ miles / day[/tex]
The standard deviation is [tex]\sigma = 5.3 \ miles \ per \ day[/tex]
The value of = 41
Generally the z-score is mathematically represented as
[tex]z = \frac{x-\= x}{\sigma }[/tex]
substituting values
[tex]z = \frac{41-46}{5.3}[/tex]
[tex]z = - 0.943[/tex]
Triangle XYZ is isosceles. Angle Y measures a°. Triangle X Y Z is shown. The lengths of sides Y X and Z X are congruent. Angle X Y Z is a degrees. What expression represents the measure of angle X? 2a StartFraction a Over 2 EndFraction 90 a 180 2a
Answer:
the answer is D.
Step-by-step explanation:
correct on edge
The expression which represents the measure of angle X is therefore; The angle x =180 - 2a.
Isosceles triangleAccording to the question;
Triangle XYZ is isosceles and Angle Y measures a°.The lengths of sides Y X and Z X are congruent.From the given information;
The measures of angle Y and Z = a.
The expression represents the measure of angle X is therefore; The angle x =180 - 2a.
Read more on isosceles triangle;
https://brainly.com/question/11884412
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
6th grade math, help me please.
Answer:
B Kim rode 3 more miles per week than Eric rode.
PLEASE DO THIS !!!!!!!!!!!!!!!!!!!!!!!!! IN THE PIC VERY EASY I GUESS PLEASEEEEEE ANSWER IT!!!!!! NO COPYING FROM ANY SOURCE THOUGH PLZZZZZZZZ! I WILL MARK BRAINLY CROWN THING IF UR ANSWER IS GOOD AND EXPLANATIONAL THANK YOUUUUU
Answer:
D. (the last one)
Step-by-step explanation:
The horizontal row lists the 3 outcomes of the spinner.
The vertial column lists the 2 outcomes of the card selection.
In the resulting sample space of 2x3=6, each table cell should contain the combination of the row value and the column value.
So in the "Orange" column, all cells below it should start with Orange. Same for the other columns.
In the Purple row, each cell should end with Purple.
Only that way, each table cell represents a possible outcome.
How many ways can 3 boys and 2 girls stand in a row so that the two girls are not next to each other?
Answer:
3 ways← key b=boy g=girlStep-by-step explanation:
b g b gg b b gg b g bgive brainllest please °∩°
The letters G, E, N, I, D, S are placed in a bag. What is the probability that the letters are randomly pulled from the bag in the order that spells DESIGN?
Answer:
The probability of randomly pulling from the bag in the order that spells DESIGN = 1/720
= 0.001389 or 0.1389%
Step-by-step explanation:
The letters placed in a bag = 6
The different ways to choose six letters are a permutation without repetition
And permutation without repetition
= 6 x 5 x 4 x 3 x 2 x 1 = 720 ways
Therefore, the probability of randomly pulling from the bag in the order that spells DESIGN
= 1/720
= 0.001389 or 0.1389%
Probability is defined as the chance that the spelling DESIGN will be pulled from a bag containing the letters: G, E, N, I, D, S, which has 720 ways to choose the letters.
Alex : Hey Bob, I think this coin is biased; I flipped it a few times and it always lends Tail. I think p, the probability of landing Head, must be less than 5%. Can you take a look?
Bob: Seriously? I bet it's fair, that is I think p = 1/2. Let me flip it three times and count the number of Heads. If the number of Heads is smaller than some threshold t, then I will buy you dinner. Otherwise, you will buy me dinner.
Alex: Wow Bob, okay! I will go ahead and reserve a fancy restaurant.
Bob: One last thing, though, just to make things fair: pick any t you want, but let's keep the proba- bility that I buy you dinner even if I'm right (that is, even if the truth is p= 1/2) below 10% please.
Alex: Go away, Bob! Stop wasting my time!
Question: why did Alex get mad?
Answer:
See below
Step-by-step explanation:
Alex finally understands how Bob was trying to trick him into winning the bet because of how he puts in the condition for probability being less than 10%. Whichever way the outcome of the coin toss turns out to be, it will be in Bob's favor and Alex will lose the bet. If the coin is flipped 3 times, the probability of having heads exactly twice is [tex]\frac{4}{9}[/tex]
Please answer this correctly without making mistakes
Answer:
The distance between the art gallery and the office supply store is 42 miles
Step-by-step explanation:
Notice that the segment that joins the office store with the art gallery, has a length that equal the distance between the art gallery and the bank, plus the distance between the bank and the office supply store. That is;
32.1 mi + 9.9 mi = 42 mi
A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item? A- 1.50 pounds B- 1.75 pounds C- 3.75 pounds D- 6.00 pounds
Answer:
D. 6 pounds
Step-by-step explanation:
$9.50-$5.00=$4.50; $4.50/$0.75= 6 pounds
Answer:
A - 1.50 pounds
Step-by-step explanation:
A potato chip company makes potato chips in two flavors, Regular and Salt & Vinegar. Riley is a production manager for the company who is trying to ensure that each bag contains about the same number of chips, regardless of flavor. He collects two random samples of 10 bags of chips of each flavor and counts the number of chips in each bag. Assume that the population variances of the number of chips per bag for both flavors are equal and that the number of chips per bag for both flavors are normally distributed. Let the Regular chips be the first sample, and let the Salt & Vinegar chips be the second sample. Riley conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. (b) t≈1.44 , p-value is approximately 0.167 (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. Select all that apply:
Answer:
(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
Step-by-step explanation:
We formulate the
H0: μ1=μ2; null hypothesis that the two means are equal and alternate hypothesis that the two mean are not equal.
Ha:μ1≠μ2 Two tailed test
Test statistic used is
t= x1`-x2` / s√n as the variances are equal and sample size is same
T value for 9 degrees of freedom for two tailed test at α = 0.05 is 2.26
P- value for t test for 9 degrees of freedom is 0.125 from the table.
Hence only a is correct .
40.) Decompose 7/8 into the sum of unit fractions.
Answer:
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
7/8 = 1/8 + 6/8
7/8 = 4/8 + 3/8
7/8 = 5/8 + 2/8
Step-by-step explanation:
Hope it helps!
The fraction 7/8 can be written as the sum of unit fraction i.e;
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
What is unit fraction?A unit fraction can be defined as a fraction whose numerator is 1.
Given fraction 7/8
can be written as the sum of the unit fraction i.e;
7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8
Hence,7/8 can be decomposed into sum of unit fraction as
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
To know more about the unit fraction click the link below:
https://brainly.com/question/15326565
#SPJ2
all summer olympics championship distamces in the triple jump from 1896 through 2012 avereged 16.38 meters, with standard deviation of 1.34 meters. what is the probability that a randomly selected distance from the distribution would fall into each of the following intervals 16.8 meters and 17.9 meters?
Answer: 0.2487
Step-by-step explanation:
Given: Mean: [tex]\mu=16.38[/tex] meters
Standard deviation: [tex]\sigma= 1.34[/tex] meters
Let X denote the distance in the triple jump.
The probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters = [tex]P(16.8<X<17.9)=P(\dfrac{16.8-16.38}{1.34}<\dfrac{X-\mu}{\sigma}<\dfrac{17.9-16.38}{1.34})[/tex]
[tex]=P(0.3134<Z<1.1343)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<1.1343)-P(Z<0.3134)\\\\=0.8717- 0.6230\ [\text{By z-table}]\\\\=0.2487[/tex]
Hence, the probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters= 0.2487
In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $8. Construct a confidence interval at a 99% confidence level.
Give your answers to one decimal place.
Answer:
The 99% confidence interval is
[tex]37.167< \= x < 44.833[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 29[/tex]
The sample mean is [tex]\= x =[/tex]$41
The sample standard deviation is [tex]\sigma =[/tex]$8
The level of confidence is [tex]C =[/tex]99%
Given that the confidence level id 99% the level of confidence is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Next we evaluate the margin of error which is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]
[tex]MOE = 3.8328[/tex]
The 99% confidence level is constructed as follows
[tex]\= x - MOE < \= x < \= x + MOE[/tex]
substituting values
[tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]
[tex]37.167< \= x < 44.833[/tex]
A train covers certain distance in two parts. Distance covered in first part is 200% more than the distance covered in second part while speed of train is in the ratio 2 : 1 in first and second part respectively. If average speed of train is 64 km/hr, then find the speed of train in first part? (in kmph)
Answer:
Part A speed=96*2=192km/h
Step-by-step explanation:
Two parts, parts A and part B
Part A=200% more than B
Let part B=x
Part A=200 more than B
=2x
Speed ratio=2:1
Average speed of train=64km/h
Let Part A speed=2x
Part B speed=x
A:B=2:1
Total ratio =3
Speed in the part A can be calculated thus:
Totatl speed= ratio of speed in part A / total ratio
64=2x/3
192=2x
x=96km/h
Part A speed=96*2=192km/h
A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste tested the new drink. a) Determine the standard error of the proportion b) What is the probability that more than 75% of consumers will indicate they like the drink
Answer:
a
[tex]S.E = 0.05[/tex]
b
[tex]P(P > 0.75) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The population [tex]p = 0.60[/tex]
The sample size is [tex]n = 96[/tex]
The sample proportion is [tex]\r p = 0.75[/tex]
Generally the standard error is mathematically represented as
[tex]S.E = \sqrt{ \frac{p(1-p)}{n } }[/tex]
substituting values
[tex]S.E = \sqrt{ \frac{0.60 (1-0.60 )}{96 } }[/tex]
[tex]S.E = 0.05[/tex]
The probability that more than 75% of consumers will indicate they like the drink is mathematically represented as
[tex]P(P > 0.75) = P(\frac{\r P - p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } } )[/tex]
The z-score is evaluated as
[tex]z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
So
[tex]P(P > 0.75) = P(Z > \frac{0.75 - 0.60 }{0.05} )[/tex]
[tex]P(P > 0.75) = P(Z > 3)[/tex]
[tex]P(P > 0.75) = 0.0013499[/tex]
This value above is obtained from the z-table
What is an equation of the line that is parallel to y=3x-8 and passes through the point (4, -5)
Hi there! :)
Answer:
y = 3x - 17.
Step-by-step explanation:
To write an equation parallel to y = 3x - 8, we need the slope as well as the coordinates of a point to solve for the "b" value in y = mx + b:
A line parallel to y = 3x - 8 contains the same slope, or m = 3.
Plug in the coordinates in (4, -5) into "x" and "y" in the equation y = mx + b respectively:
-5 = 3(4) + b
-5 = 12 + b
Simplify:
-5 - 12 = b
b = -17.
Rewrite the equation:
y = 3x - 17.