Step-by-step explanation:
we have p=proportion of vegetarian students=0.08
a. FALSE.
for normal approximations we must have np>=5 and n(1-p)>=5
here n=60 so np=60*0.08=4.8 which is less than 5.
hence normal approximation is not applicable.
b. TRUE.
for binomial proportion , the distribution is right skewed if 1-2p>0 or, 0.5>p
here, p=0.08 so 0.5>p is satisfied. hence it is rightly skewed.
c. FALSE.
here, n=125 which is quite large. hence normal approximation is applicable.
let phat be the sample proportion
then phat approximately follows a normal distribution with E[phat]=p=0.08
and variance=V[phat]=p(1-p)/n=0.08(1-0.08)/125=0.0005888
hence standard deviation=sqrt(0.0005888)=0.0242652
hence effective range of phat is [0.08-3*0.0242652,0.08+3*0.0242652]=[0.0072044,0.1527956]
12%=0.12 lies in this effective range.
hence it is not unusual.
In this exercise we have to classify whether the statements are true or false:
a) False
b) True
c) False
d) False
e) False
We have: [tex]p=proportion of vegetarian students=0.08[/tex]
a) FALSE.
For normal approximations we must have:
[tex]np\geq 5 \\n(1-p)\geq 5[/tex]
Where [tex]n=60[/tex] so [tex]np=60*0.08=4.8[/tex] which is less than 5. Hence normal approximation is not applicable.
b)TRUE.
For binomial proportion , the distribution is right skewed if :
[tex]1-2p>0 \\ 0.5>p[/tex]
Where, p=0.08 so 0.5>p is satisfied. hence it is rightly skewed.
c) FALSE.
Where, n=125 which is quite large. hence normal approximation is applicable. Let phat be the sample proportion then phat approximately follows a normal distribution with:
[tex]E[phat]=p=0.08[/tex]
and [tex]variance=V[phat]=p(1-p)/n=0.08(1-0.08)/125=0.0005888[/tex]
Hence standard deviation [tex]=sqrt(0.0005888)=0.0242652[/tex]
hence effective range of phat is:
[tex][0.08-3*0.0242652,0.08+3*0.0242652]=[0.0072044,0.1527956][/tex]
12%=0.12 lies in this effective range. Hence it is not unusual.
d) FALSE.
e) FALSE.
See more about proportion at : brainly.com/question/8704765
What is the arc measure of PQ?
Answer:
47.1
Step-by-step explanation:
l= rø
or, l= 18 × 5π/6
or, l= 15π
l = 47.1
HELP ME PLEASE TO THIS QUESTION
Answer:
510 miles, 204/3 = 68
68x7.5= 510
There u go :)
Please fill this all im for 20 points! <3 :)
Answer:
Step-by-step explanation:
1) Regular price = $ 20
Reduction = 18% of regular price
= 0.18 * 20
= 3.6
Discount price = 20 - 3.6 = $ 16.4
2) Regular price = $ x
Reduction = 18% of regular price
= 0.18 * x
= 0.18x
Discount price =$ (20 - 0.18x)
3) Discount price = $ 18.45
Let the regular price be x
(100 - 18)% of x = 18.45
82% of x = 18.45
[tex]\frac{82}{100}*x=18.45\\\\ x = 18.45* \frac{100}{82}\\\\ x = 22.50[/tex]
Regular price = $22.50
A coin bank has 17 coins that contains only dimes and quarters. The coins are worth $3.35. How many of each coin are in the bank?
Answer:7 quarters and 6 dimes
Step-by-step explanation:
The average weight of 3 books is
3/gm, one book weighs 3'/«gm
and the second 5/2gm. What is the
weight of the third?
The weight of the third book is approximately 5.33 grams.
How to calculate the valueAccording to the given information:
The average weight of the 3 books is 3 grams.
To find the average weight, we sum up the weights of all the books and divide by the total number of books:
(1/3 + 5/2 + x) / 3 = 3
Now we can solve this equation to find the weight of the third book:
(1/3 + 5/2 + x) = 3 * 3
(1/3 + 5/2 + x) = 9
(1 + 15 + 6x) / 6 = 9
(22 + 6x) / 6 = 9
22 + 6x = 54
6x = 54 - 22
6x = 32
x = 32 / 6
x ≈ 5.33
Therefore, the weight of the third book is approximately 5.33 grams.
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The average weight of 3 books is 3gm, one book weighs 1/3 gm and the second 5/2gm. What is the weight of the third?
The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commuting times are normally distributed and that the standard deviation is 6.1 minutes, calculate the probability that a randomly selected commuter spends for the following cases.
1. More than 31 minutes commuting one way.
2. Less than 8 minutes commuting one way.
Answer:
1. 0.1635
2. 0.0026
Step-by-step explanation:
The computation of the probability in the following cases are as follows:
1.
Given that
Mean = 25 minutes
ANd, the standard deviation is 6.1 minutes
So here the z score would be
= (31 - 25) ÷(6.1)
= 0.98
Now the probability is
= P(Z>0.98)
= 0.1635
2. the z score would be
= (8 - 25) ÷(6.1)
= -2.79
Now the probability is
= P(Z<-2.79)
= 0.0026
1. A company has a cash portfolio measured in millions. The drift is 0.1 per month, variance is 0.16per month. The initial cash is 2.0. a) Find the probability distribution after 6 months and after 1 year. b) Find the probability of a negative cash position at the end of 6 months and the end of 1 year. c) At what time in the future is the probability of a negative distribution greatest.
Answer:
Step-by-step explanation:
From the information given:
The probability distribution at the end of 6 months is determined as follows:
After 6 months;
Mean of probability distribution = value of Initial cash + [tex]\alpha[/tex]T
=2.0 +(0.1 × 6)
=2.6
After 6 months;
The probability distribution's standard deviation is estimated by using the following formula:
Standard deviation:
[tex]= b\sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{6}[/tex]
= 0.9798
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 2.6
Standard deviation 0.9798
Variance 0.96
After 12 months, the probability distribution is as follows:
Mean = value of Initial cash + [tex]\alpha[/tex]T
= 2.0 +(0.1 × 12)
= 3.2
The standard deviation is:
The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{12}[/tex]
= 1.3856
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 3.2
Sandard deviation 1.3856
Variance 1.92
b)
in 6-month distribution, the probability of the negative value of the cash position is as follows.
Now, for us to find the negative cash distribution;
We need to estimate the z -scores value.
The z-score inform us greatly on the concept of how far a particular data point is from the mean.
For a normal distribution;
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
Here;
the value of x = zero as a result that if it exceeds zero. the cash position will be negative.
∴
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]
[tex]z = -2.6536[/tex]
Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.
As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.
For 12 months distribution:
The Probability of negative cash position is calculated as follows:
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]
Using the standard distribution tables,
N(-2.31) equals 0.0104 or 1.04 percent.
As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year
c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]
This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.
To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.
The first step is to go over the z-score formula in more detail, as seen below.;
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]
Now, compute the derivative of this equation with respect to T as follows:
[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]
Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:
[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]
As a result, the time period in which achieving a negative cash condition is = 20 months.
Two consecutive integers have a product of 12. What is the initial equation that would be used
to solve this?
x² = 12
x(x + 1) = 12
2 (2+2) = 12
x(x − 2) = 12
Answer:
x(x+1) = 12
Step-by-step explanation:
If a number is x then it's consecutive number will be x + 1.
And their product x(x+1)
Jeff has a square piece of art paper. He cuts across it from one corner to the opposite corner to make two pieces. What is the total number of sides and angles in both of the new shapes?
Answer:
The number of sides is 3 on each piece of paper, altogether there are 6 sides.
The total number of angles on a triangle is 180°, altogether the sum of both triangles is 360°
Christopher has a garden in the shape of a square with a side length of 24 feet. He plans to plant tomatoes along the
diagonal. How long is the diagonal of Christopher's garden?
A - 48 Ft
B - 24 Ft
C - 24 square root of 2
D - 24 square root of 3
9514 1404 393
Answer:
C - 24 square root of 2
Step-by-step explanation:
In case you haven't memorized the fact that the diagonal of a square is √2 times the side length, you can figure it from the Pythagorean theorem.
d² = s² + s² . . . . square of hypotenuse is sum of squares of sides
d² = 2s²
d = s√2 = (24 ft)√2 = 24√2 ft
You can complete one-sixth of a task in an hour. Your friend can complete one-sixth of the same task in an hour. How long will it take to complete the task if you work together?
Answer:
3 hours
Step-by-step explanation:
there's 6 parts and it takes them both an hour for each part so alone they would take 6 hours but divide that by 2 and it's 3 hours
Answer: I would say 3 hours if you worked seperatly from each other to complete one task
Step-by-step explanation:
Use the Quadratic Formula to solve the equation x^2-15=2x
Answer:
x= -3
y= 5
Explanation:
Move the 2x to the left by subtracting it by itself
you should get x^2 -15 - 2x =0
That's it in standard form
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answer:
Its only 5 point but ok
its $3.44 per quart
Step-by-step explanation:
round off all answer in to two decimal places A=p(1+in) Steven won a portion of the local lottery.the price money is to the value of R18000.he wants to invest the money but does not know which bank to choose. FNB offers Steven 5,6/% for 8 years simple interest per annum, Nedbank offers Steven 6,6% for 6 years simple interest per annum and standard bank offers 7,2% for 5 years simple interest determine each bank future value to help Steven decide which bank he should choose FNB NEDBANK STANDARD BANK
Answer:
FNB bank
Step-by-step explanation:
FNB = 18000 * 0.056* 8 = 8064
Nedbank = 18000*0.066* 6 = 7128
Standard = 18000*0.072*5=6480
FNB is the best choice for Steven
Solve for x: wx-x=d
PLEASE HELP NEED ASAPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRR
Answer:
wx-x=d
wx = d + x
x = d/w + x/w
Step-by-step explanation:
Answer:
x = d/(w-1)
Step-by-step explanation:
factor out 'x' as first step:
x(w - 1) = d
now divide by w-1:
x = d/(w-1)
If y’all could help on this one that would be great, no rush I have a week to turn in just make sure it’s correct and explains it I will give 50 points, thank you :)
ANSWER
-1,-1 is P
-4, -3 is R
-2, -3 is Q
I think this is the answer hope it helps :)
What is the square unit of 6 by 9 square unit what is the area?
Answer:
54 unit ^2
Step-by-step explanation:
Well a formula for a rectangle is a=lw
So 6*9=54
The area is 54
Please help! What is the volume of the triangular pyramid?
Answer and explanation please! <3
Answer:
30cm3
Step-by-step explanation:
Volume=Base area *height
Base area is a triangle=1/2 *base*height
1/2*3*4=6cm2
Height=5cm
Volume=6*5=30cm3
Answer:
10 m³
Step-by-step explanation:
My apologies for attaching the explanation in a pic, brainly wouldn't let me upload my text answer for some reason.
Find the value of x.
(a)
(10.7)" = 2
3x92x1 = 27*
(b)
Step-by-step explanation:
where is x in the question
Which triangles are similar to triangle ABC ?
Answer:
The answer is A
Step-by-step explanation:
Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.
Mr Soto bought some dvds each DVD cost 13.55 if Mr Soto did not spend more Thales 75$ which inequality could be used to find d the number of DVDs Mr. Soto bought
Answer:
c
Step-by-step explanation:
C is the only equality that no matter what, the value would be $75 or less
someone please help me answer this!!
Answer:
17 units is the answer
Step-by-step explanation:
Points are (1,9) and (9,-6)
Pythagorean theorem can be written as,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(9-1)^2 + (-6-9)^2}\\\\d=\sqrt{(8)^2+(15)^2} \\\\d=\sqrt{64+225} \\\\d=\sqrt{289} \\\\d=17[/tex]
∴ d = 17 units is the distance between 2 points.
please help me i’ll give brainliest
Answer:
105 degrees
Step-by-step explanation:
You need to understand the properties of corresponding angles and supplementary angles.
ANSWER ASAP! NO SCAM LINKS OR REPORTED.
Answer:
d
Step-by-step explanation:
it would be a parabola not linear
On his last 5 math tests, Gilbert earned: 94, 72, 83, 94, 90. What was his average score? ( Report your answer to the tenths place).
Answer:
Average of Gilbert in last 5 test = 86.6
Step-by-step explanation:
Given:
Score earned by Gilbert in last 5 test = 94, 72, 83, 94, 90
Find:
Average of Gilbert in last 5 test
Computation:
Average value = Sum of all events / Total number of events
Average of Gilbert in last 5 test = Sum of all last results / Number of results
Average of Gilbert in last 5 test = [94 + 72 + 83 + 94 + 90] / 5
Average of Gilbert in last 5 test = [433] / 5
Average of Gilbert in last 5 test = 86.6
Solve for x. Assume that lines which appear tangent are tangent.
Presumably, x is standing in for the question mark.
The pair of vertical angles (DFE and CFV) shown here both have measure 125°. This angle measure is equal to the average of the measures of the arcs intercepted by the chords CE and DV.
So we have
angle DFE = 1/2 (arc CV + arc DE)
125° = 1/2 (x + 200°)
250° = x + 200°
x = 50°
Estimate 2.21x5.1 i guess need help please I don’t want to fell this class
Answer:
10
Step-by-step explanation:
Im guessing since you have to estimate it then u have to round them up. So if you move both of their points by 2 spaces (divide both by 100) They will be 221x510.
Round them up to 200x500.
That woule be 100 000. Then at the end just dont forget to divide by 10000.
Hope this was helpful
for each of the following find the missing sides
Answer:
the missing side is 90 because is a right triangle
The following is a data set of five quiz scores.
92, 88, 90, 96, 84
What is the mean absolute deviation of the scores?
Answer:
The mean absolute deviation is 36.8. Hope this was helpful
Step-by-step explanation:
The probability that Ismael makes a basket is 7/10. If he shoots 100 baskets, how many can he expect to make?
Answer:
70 baskets
Step-by-step explanation:
Let b be the number of baskets he will make if he shoots 100 baskets.
[tex]\frac{7}{10} =\frac{b}{100} \\700=10b (now divide by 10 from both sides)\\[/tex]