Answer:
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Step-by-step explanation:
Subtraction of normal variables:
When we subtract two normal variables, the standard deviation is the square root of the sum of variances of each variable.
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.
Sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6.
The standard error for this sample is:
[tex]s_b = \frac{1.6}{\sqrt{195}} = 0.1246[/tex]
Sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
The standard deviation for this sample is:
[tex]s_a = \frac{2.1}{\sqrt{143}} = 0.1756[/tex]
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
[tex]s = \sqrt{s_a^2 + s_b^2} = \sqrt{0.1756^2 + 0.1246^2} = 0.2153[/tex]
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Answer:
sqrt [ (1.6^2)/195 + (2.1^2)/143 ]
An elevator has a placard stating that the maximum capacity is 1580 lb-10 passengers. So, 10 adult male passengers can have a mean weight of up to 1580/10 = 158 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 158 lb. (Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.) Does this elevator appear to be safe?
Answer:
a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb
b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
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 zscore 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 pvalue, 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.
Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.
This means that [tex]\mu = 160, \sigma = 35[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]
a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.
This is 1 subtracted by the pvalue of Z when X = 158. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 160}{11.07}[/tex]
[tex]Z = -0.18[/tex]
[tex]Z = -0.18[/tex] has a pvalue of 0.4286
1 - 0.4286 = 0.5714
0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.
b.) Does this elevator appear to be safe?
No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
(PLEASE HELP)James tosses a coin 50 times. It lands on heads 23 times and on tails 27 times.
What is the relative frequency of the coin landing on heads in this experiment?
A 23%
B 46%
C 50%
D 54%
Answer:
b
Step-by-step explanation:
WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.
Answer:
8
Step by Step Explanation
Answer and Step-by-step explanation:
To find Z, we have to use the trigonometric function of Sine.
The Sine trig function looks like this:
sin(Angle) = [tex]= \frac{opposite.side}{hypotenuse}[/tex]
Plug in the values and solve for z.
[tex]sin(30) = \frac{4}{z} \\\\\\\\\\z = \frac{4}{sin(30)}[/tex]
Plug into a calculator and solve.
We get z to be 8.
#teamtrees #PAW (Plant And Water)
Helppp pleaseeee which one
Answer:
Coefficient is your answer
Answer:
3 is a coefficient
Step-by-step explanation:
a constant is a number without a variable and that is unchanging
3 has the variable w attached to it and will change with the value of w
hope this helps <3
Please need help thank
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
It has the most x's (rolls) compared to the other numbers rolled.
Point P is shown graphed on the coordinate grid as (6,4). In relation to point P, point A is located 2 units closer to the origin along the x-axis and 2 units farther from it along the y-axis. What would be the location of point A ?
Answer:
The coordinates of point A are [tex]A(x,y) = (4,6)[/tex].
Step-by-step explanation:
The location of point A is defined by the vectorial sum of absolute coordinates of point P and coordinates of point A relative to coordinates of point P, that is:
[tex]A(x,y) = P(x,y) + \vec v_{PA}[/tex] (1)
[tex]P(x,y)[/tex] - Absolute coordinates of point P.
[tex]A(x,y)[/tex] - Absolute coordinates of point A.
[tex]\vec v_{PA}[/tex] - Vector to point A relative to point P.
If we know that [tex]P(x,y) =(6,4)[/tex] and [tex]\vec v_{PA} = (-2, 2 )[/tex], then the absolute coordinates of point A are:
[tex]A(x,y) = (6,4) +(-2,2)[/tex]
[tex]A(x,y) = (4,6)[/tex]
The coordinates of point A are [tex]A(x,y) = (4,6)[/tex].
Help asappppp !!!!!!!!
Answer:
None
Step-by-step explanation:
2(x + 10) - 17 = 2x - 2
simplify:
2x + 20 - 17 = 2x - 2
2x + 3 = 2x - 2
subtract 3 from both sides of the equation:
2x = 3x -5
no solution
URGENT PLEASE, I NEED THIS FOR A TEST RIGHT NOW- A jar one-fifth filled with water weighs 560g. The same jar four-fifth filled with water weighs 740g. What is the weight of the empty jar??
Answer:
493g.
Step-by-step explanation:
what is 47 ÷ 12 1/3 =
Answer: 47/363
(Decimal: 0.129477)
On a drive from one city to another, the person averaged 51 mph. If he had been able to average 72 mph, he would have reached his destination 7 hrs earlier. What is the driving distance between one city and the other?
Answer: 1224 miles
Step-by-step explanation:
Given
the average speed of a person is 51 mph
If speed is increased to 72 mph, he would have reached 7 hr earlier
Suppose d and t be the distance and time taken
[tex]\Rightarrow t_1=\dfrac{d}{51}[/tex]
If the speed is 72 mph
[tex]\Rightarrow t_2=\dfrac{d}{72}[/tex]
Also, [tex]t_1-t_2=7[/tex]
[tex]\Rightarrow \dfrac{d}{51}-\dfrac{d}{72}=7\\\\\Rightarrow \dfrac{1}{51}-\dfrac{1}{72}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{24-17}{1224}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{7}{1224}=\dfrac{7}{d}\\\\\Rightarrow d=1224\ miles[/tex]
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error (in cm2) in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism? Enter your answer in the box.
Answer is in the file below
cutt.us/brainly
A=352in2
A=2(wl+hl+hw)=2·(8·12+4·12+4·8)=352in²
A scientist measured a museum specimen. She recorded the measurement as 75 centimeters. What could the scientist have been measuring? length of a dinosaur bone
mass of a dinosaur bone
length of a gem
mass of a gem
Answer:
75cm is the measurment
Step-by-step explanation:
It would have had to have been the lenght of the gem because 75cm or 75 centimeters is a measurment not the mass of something. The mass is the amount of matter in an object.
What is the CONSTANT in the expression 3k + 12?
Answer: 12
Step-by-step explanation:
The constant of the expression is 12.
What is a constant?'A constant is a value or number that never changes in expression that is it's constantly the same.'
According to the given problem,
In the expression 3k + 12 , k is a variable. A variable is a quantity that may change with respect to the mathematical criteria.
If k = 1, the value of the expression is (3 × 1) + 12 = 15
k =2, the value is (3 × 2) + 12 = 18
But we can see that no matter the value of k is, the expression has to be added with 12.
Hence, we can conclude that since the value of 12 does not change irrespective of the changing values k, the constant of this expression is 12.
Learn more about constant here:
https://brainly.com/question/18650947
#SPJ2
Geometry Question, Need help. Will give brainliest.
Answer:
i cant see the direction sorry :(
Step-by-step explanation:
A school has to select one student to take part in a General Knowledge Quiz.Kelly and Rory took part in six trial quizzes. The following lists show their scores.Kelly 28 24 21 27 24 26Rory 33 19 16 32 34 18Kelly had a mean score of 25 with a range of 7.(a) Calculate Rory's mean score and range.(b) Which student would you choose to represent the school? Explain thereason for your choice, referring to the mean scores and ranges.
please help! I really need it if you can tysm
Answer:
Step-by-step explanation:
Half of the animals are cats. If they take in 5 cats, then the total number of animals is 2×5 = 10.
If they take in 8 animals, the number of cats is ½ of 8 = 4.
If they take in 6 cats, then the total number of animals is 2×6 = 12.
If they take in 16 animals, the number of cats is ½ of 16 = 8.
A rectangle has a base of 4 feet and a height of 30 inches.
What is the area of the rectangle? Choose the correct answer below.
A
4.5 square feet
B
10 square feet
C
46 square inches
D
120 square inches
In a local middle school, there are 20 Science teachers, 30 Social
Studies teachers and 600 students. What is the ratio between the number
of Science teachers and the number of students for this school? *
1:12.
1:30
1:35
1:40
Answer:
no of science teachers is 20
no of students is 600
ratio=20/600
=20:600
=1:30
pls give me brainliest
AccelGR7_Math_T6_FSQ_OL_FY21
Look at this system of linear equations.
S2x + 3y =-4
ly = 2x +4
What is the solution to the system of linear equations?
X = -2, y = 0
x= – 1, y = 2
x = 4, y = - 4
x = 2, y = 8
Answer:
x=-2 and y =0
Step-by-step explanation:
2x + 3y=-4
y=2x + 4
2x -y = -4
4y= 0
y = 0
2x -0=-4
2x =-4
x=-2
and the black flaure the ima Name a possible rotation and the degree in which it turned
Answer is in the file below
tinyurl.com/wpazsebu
Question 5. What is the mean of 51, 60, 80, 32, 47, 30 * A.50 B.6 c. 60 D40
Answer:
A (50)
Step-by-step explanation:
Mean is the total numbers added up divided by the # of numbers.
There are 6 numbers.
51 + 60 + 80 + 32 + 47 + 30 = 300
300/6 = 50
Therefore, the answer is A.
Answer:
A
Step-by-step explanation:
Because to find the mean you add up all the numbers.
51+60+80+32+47+30=300
Then your suppose to divide by the sum.
300/6=50
Write two fractions that have a sum of 1 and have different denominators.
Answer:
1/5+8/10=1
Step-by-step explanation:
1/5 = 2/10
Select the improper fraction that is not equivalent to the whole number 6
18/3
6/1
54/3
54/9
Answer:
54/3=18
Step-by-step explanation:
18/3=6
6/1=6
54/9=6
Washe
car alone, ustin takes
45 hours
had
takes tos hours.
How
donde long does the car
by
does it take Justin's
hiods?
Washing car alone it takes Justin 4.5 hours. If his dad helps him it takes 1.5 hours. His long does it take Justin’s dad to wash the car by himself?
Answer:
it takes his dad 3 hours
Step-by-step explanation:
4.5-1.5 =3
Find the coordinates of the point (a, b).
a = ?
(0, 1)
0 1
2
(a, b)
O v2
O v2
2.
1(-1,0)
रा
45°
DONE
(1,0)
b= ?
1
O v2
O v2
2.
Зл
2
(0, -1)
9514 1404 393
Answer:
(a, b) = (√2/2, √2/2) . . . . . choice C in each case
Step-by-step explanation:
The points on a unit circle will not have coordinate values greater than 1 (eliminates √2). The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° are ...
(cos(45°), sin(45°)) = (a, b) = (√2/2, √2/2)
The coordinate of point (a, b) is (√2/2, √2/2)
Coordinate of a point on a circleNote that the points on a unit circle will not have coordinate values greater than 1.
The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° is given according to the coordinate point (cos45, sin45)
a = cos45 = √2/2
b = sin45 = √2/2
Hence the coordinate of point (a, b) is (√2/2, √2/2)
Learn more on unit circle here: https://brainly.com/question/23989157
solve please
due very soon
need done asap
Answer:
B
Step-by-step explanation:
Both triangles are similar. The similarity ratio between AB and EF is 4, which must mean that FG is BC (60)/4. The area of a rectangle is base x height -> 6.25 x 15 = 93.75 square cm
Hope this helps!
HELP ME NOW PLEASE!!!!!
The question says "State the coordinates of Point G after a rotation of 90 degrees clockwise followed by a dilation with scale factor 2." The coordinates are G(4.5, 3).
Answer:
Hiiiiiiiiiiiii Picture pls?
Step-by-step explanation:
:))
Please help me I don’t understand
Answer:
x= 230
Step-by-step explanation:
since a circle is 360 degrees
x + 130 = 360
x= 360 -130
x=230
Helppppppppppp I have 3 minutes
Answer:
It definitely is linear, and it is a straight line
Step-by-step explanation:
Try using desmos, it may help
Answer:
A) it is linear and it is a straight line
Step-by-step explanation:
it is a linear equation. It will be straight
y=mx+b is linear