Answer:
a) Approximately normal variable.
b) 0.05.
c) 0.0123
d) Approximately 0% probability that more than 10% of her sample will be Snorlaxes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using 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 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
5% chance that a Snorlax will appear. Tanya will search Mill Creek park until she captures 312 random pokemon.
This means that [tex]p = 0.05, n = 312[/tex]
a. What type of random variable can we use to approximate the sample proportion?
By the Central Limit Theorem, an approximately normal variable.
b. What is the mean of the sample proportion?
[tex]\mu = p = 0.05[/tex]
The mean is 0.05.
c. What is the standard deviation of the sample proportion?
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{312}} = 0.0123[/tex]
d. What is the approximate probability that more than 10% of her sample will be Snorlaxes?
This is 1 subtracted by the pvalue of Z when X = 0.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1 - 0.05}{0.0123}[/tex]
[tex]Z = 4.05[/tex]
[tex]Z = 4.05[/tex] has a pvalue of approximately 1
1 - 1 = 0
Approximately 0% probability that more than 10% of her sample will be Snorlaxes
Find the sum of the measures of the interior angles of the indicated covex
Very confused
Answer:
Step-by-step explanation:
Hope it helps u!!
12 bars of soap for $8.69
3/2 of a number is less than this number?
true or false, justify your answers
Answer:
False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2
Answer:
false
if the number is X
3/2 of X= X 1/2
[tex]x \frac{1}{2} > x[/tex]
4.
What is the equation of the circle with a radius of 5 and center at (2, 3)?
AO (x + 2)2 + (y + 3)2 = 25
BO (x - 2)2 + (y - 3)2 = 25
CO (x - 2)2 + (y - 3)2 = 5
D. (x + 2)2 + (y + 3)2 = 5
Answer:
the answer is A
Step-by-step explanation: since the radius is 5 and we have (2,3) then we are going into 2 and 3 the x and y represent 5 so the answer wouldn't be 5 then you would have done no work. so it is A. i suck at explaining things hope this helps!
Step-by-step explanation:
[tex]general \: equation \\ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0 \\ centre : ( - g, - f) = (2,3) \\ g = - 2 \: and \: f = - 3 \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = {( - 2)}^{2} + {( - 3)}^{2} - {(5)}^{2} \\ = - 12 \\ therefore \\ {x}^{2} + {y}^{2} - 2x - 3y - 12 = 0[/tex]
Estimate the slope of the regression line manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime in thousands of holes drilled of bits at different speeds in surface feet per minute (sfm). Suppose you want to create a model that estimates the drill bit lifetime ( y) based on rotation speed ( x). Summary statistics for 20 observations collected are given below.
20 20 20 20
Σ xi = 2,000 ; Σ yi = 86.6 Σ xi^2= 216,000 Σ xiyi= 8,338
i= 1 i=1 i=1 i=1
Estimate the slope of the regression line.
a. -0.017
b.-0.037
c. -0.057
d.-0.077
Answer:
[tex]b_i = -0.020125[/tex]
Step-by-step explanation:
Given
[tex]\sum x_i= 2000[/tex]
[tex]\sum y_i= 86.6[/tex]
[tex]\sum x_i^2= 216000[/tex]
[tex]\sum x_iy_i = 8338[/tex]
[tex]n = 20[/tex]
Required
Determine the slope (b) of the regression line
This is calculated as:
[tex]b_i = \frac{\sum xy - \frac{\sum x\sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}}[/tex]
Substitute values for each term, we have:
[tex]b_i = \frac{8338 - \frac{2000 * 86.6}{20}}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the numerator
[tex]b_i = \frac{8338 - 8660}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the denominator
[tex]b_i = \frac{8338 - 8660}{216000 - 200000}[/tex]
[tex]b_i = \frac{-322}{16000}[/tex]
[tex]b_i = -0.020125[/tex]
3. The cost of renting a car is $26.50 plus $10 per day. Sales tax is 6%. Select all expressions that represent the cost of renting a car for d days. 1.06(26.50 + 100) 28.09d 26.50 + 6d 28.09 + 10.6d 26.50 + 1.06d
Can I please get some help on this pretty please
Answer:
Score with 6 questions wrong :
= 40 - (6×2)
= 40 - 12
= 28
Score with x questions wrong :
= 40 - (x×2)
= 40 - 2x
a) Expand and simplify (x + 4)(x - 7)
Answer:
X x X=x²
X x -7=-7x
4 x X=4x
4 x -7=-28
-7x + 4x=-3x
x² + -3x -28
hope that helped :)
Step-by-step explanation:
A sphere has a radius of 9 in, which means its volume is 972π in3. The sphere is dilated by 2⁄3. What is the volume of the new sphere?
Answer:
08-Oct-2009 — If a spherical balloon has a volume of 972 pi cubic centimeters, what is ... is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=972pi r=9 ... and it is good to know the squares of the next 10 numbers.
Answer:
I have this same question on my math test.
Since the radius is 9, the diameter is 18.
The shape is being dilated by 2/3, so the new radius is 6.
Volume formula: V = 4/3πr^3
So now we plug in the values.
V = 4/3 x π x (6)^3
V = 4/3 x π x 216
V = 288π
If the answers do not have the pi symbol present, then it has been multiplied into the answer.
288 x 3.14 = 904.32
The new volume of the sphere is 904.32 in^3
Two trains, Train A and Train B, weigh a total of 243 tons. Train A is heavier than Train B. The difference of their weights is 87 tons. What is the weight of each train?
Answer:
Train A weighs 156 tons, and Train B weighs 78 tons.
Step-by-step explanation:
Given that two trains, Train A and Train B, weigh a total of 243 tons, and Train A is heavier than Train B, with a difference of their weights of 87 tons, to determine what is the weight of each train, the following calculation has to be done:
(243 - 87) / 2 = B
156/2 = B
78 = B
243 - 87 = A
156 = A
Therefore, Train A weighs 156 tons, and Train B weighs 78 tons.
What’s the answer for this please I need it
Step-by-step explanation:
each week kyle saves $5.00
The Hutton's records for the past six months show that their expenditures totaled $2.768, $3,001, $2,663, $2,471, $2,893, and $2,803. What is their average monthly expenditure for the six months?
Answer
2766.5
Step-by-step explanation:
Well to solve for average all you have to do is add the values together then divide by the number of values you started with. So we add them together(2768+3001+2663+2471+2893+2803) and get 16599. Then, since there were 6 values we divide that by 6 and you get your answer.
Answer this question pls!!
Answer:
(6, 7)
Step-by-step explanation:
A rectangle means that opposite sides are parallel to each other and that opposite sides are equal in measurements.
If we look at the opposite side starting at (2, 1), we can count how long the other side should be. Counting the next point of the rectangle is (6, 1) which is a difference of 4. This means if we count from (2, 7) 4 spaces to the right, we will find our missing vertex.
(2 + 4, 7) = (6, 7)
Round to the nearest hundredth (2 decimal places) when necessary
Answer:
volume = 91 cm²
perimeter = 41.1 in
Step-by-step explanation:
volume = 1/2(b1+b2)(h) = 1/2(11 + 15)(7) = 91 cm²
Marking brainliest please help me
Answer:
I think B
Step-by-step explanation:
Not sure but seems like so. Hope I helped U :)
no link nor file pease help im crying about these questions
Answer:
7
Step-by-step explanation:
10.5*2/3= 3.5*2=7
Answer:
Step-by-step explanation:
WILL MARK BRAINLEST Select the correct answer.
The stem and leaf plot shows the number of coples of a newly released book ordered from several bookstores.
Answer:
the median is 139
Step-by-step explanation:
there are 19 numbers in the data set. Therefore, the 10th number would be the median.
PLEASE HELP!!!!!!! Will mark brainlest!!!
Answer:
Step-by-step explanation:
78-90 = 12
Please help!
1. What is the perimeter of the triangle below? Show your work.
Answer:
16.73 I THINK
Step-by-step explanation:
my guess is n1 is relating to the 4.9, and if it then you would do the Pythagorean theorem. because the degrees are there to let you know it's a right angle and you are able to use the theorem..... so -
4.9^2 + 4.9^2 =C^2
48.02 =C
√48 = 6.93 (rounded to nearest hundredth)
then you add them all together
4.9+4.9+6.93=16.73
Can someone help me with this please ?
Answer:
I think it’s A.
Step-by-step explanation:
ASCD is a parallelogram. Determine whether each statement must be true. Select Yes
or No for each statement
B
Answer:
angel DAC=angle BAC because opposite angle of parallelogram is equal
In what direction does the function f(x)=−(14x−1)(4x+1) open? Explain.
Answer: Direction opens downward
Step-by-step explanation:
X-Intercept: (1/14,0),(-1/4,0)
Y-Intercept: (0,1)
Find the vertex using x= -b/2a
Plug it into the vertex form = y=a(x-h)^2 +k
H,K will identify the direction.
A train can accommodate at most 80 passengers, economy class (x) and firstclass (y) passengers. To avoid making a loss the train must carry at least ten
economy class passengers and at least twenty first class passengers. Due to the
number of complementary items the first-class passengers receive, the number
of first-class passengers should be at most three times the number of economy
class passengers.
First class tickets cost N$5000 while economy class tickets cost N$3000.
i) State/ describe what the variables x and y represent.
ii) State the objective function.
iii) List the constraints.
Answer:
Step-by-step explanation:
1) (x) is economy class and (y) is first class
2) The objective function is to avoid making a loss in prophet making the train have the avalibility for 10 economy class passengers and at least 20 first class passengers.
3) The constraints are that there are only 10 spots for economy class and at least 20 for first-class passengers.
What is the area of this composite figure?
A) 130 in2
B) 280 in2
C) 436 in2
D) 616 in2
Answer:
See explanation. I attached a photo to help visualize and make it easier to understand, but tell me if handwriting was fine :)
Also, C) 436 in² is correct :)
Step-by-step explanation:
the answer is C
Step-by-step explanation:
if we take the 15 from 28
13 will be left
so 13×22=286
and 15×5=75
15×5=75
150+286=436
hopefully its helpful
Help plis I don’t understand ✋✋
Trapezoid Area =
[ ( Sum of the rules ) × ( height ) ] ÷ 2
_________________________________
Area = [ ( 2 + 3 ) × 3 ] ÷ 2
Area = [ 5 × 3 ] ÷ 2
Area = 15 ÷ 2
Area = 7.5 m^2
8
The median of 3 numbers is 7. If one of the numbers is 10, which of the following is a possible value for one of
the other numbers?
0/
6
8
ОООО
13
17
Review Questions
Mathematics
9514 1404 393
Answer:
(a) 6
Step-by-step explanation:
The median is the middle number when they are sorted into order. If one of the numbers is 10, the remaining number must be any number less than 7. Of the offered choices, the only one less than 7 is 6.
__
The three numbers are 6, 7, 10.
Find the area and perimeter
Answer:
Step-by-step explanation:
Add all 4 sides to get perimeter so the first one is 9+9+2+2=22cm
the area is length x width so the first one is 9 x 2 =18cm ^2
For each expression in the table, select which number line model, If any, can be used to represent the expression. Select all appropriate cells in the
table.
Answer:
I don’t know
Step-by-step explanation:
You didn’t attach a photo lol
7) Write an inequality that represents 7 more than three times a number, n, is less than 16.
Answer:
3n + 7 < 16
Step-by-step explanation:
7 more than 3 times a number, n, is less than 16 is represented by
3n + 7 < 16 where:
3n = three times a number, n,
+ 7 = 7 more than
and
< 16 = is less than 16.
Answer:
Step-by-step explanation:
NEED HELP DUE IN 2 MINUTES!!!!
A cube has a volume of 64 cubic feet. What is the length of one side of the cube in feet?
Answer:
4 feetStep-by-step explanation:
s³ = 64
Take the cube root of both sides
s = 4