A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 52.5 mm and a standard deviation of 2.5 mm. What percent of the butterflies had the following wingspans? A. Less than 48.9 mm B. Between 49 and 55
Answers
Answer:
A. 7.5%
B. 68.26%
Step-by-step explanation:
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.
Mean of 52.5 mm and a standard deviation of 2.5 mm.
This means that [tex]\mu = 52.5, \sigma = 2.5[/tex]
A. Less than 48.9 mm
The proportion is the pvalue of Z when X = 48.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48.9 - 52.5}{2.5}[/tex]
[tex]Z = -1.44[/tex]
[tex]Z = -1.44[/tex] has a pvalue of 0.075
0.075*100% = 7.5%, which is the answer.
B. Between 49 and 55
The proportion is the pvalue of Z when X = 55 subtracted by the pvalue of Z when X = 49. So
X = 55
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 52.5}{2.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 49
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 52.5}{2.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826*100% = 68.26%, which is the answer.
The percent of the butterflies had the given wingspans are;
A) 7.5%
B) 76.64%
We are given;
Population mean; μ = 52.5 mm
Population standard deviation; σ = 2.5 mm
Formula for z-score is;
z = (x' - μ)/σ
A) For less than 48.9 mm,P(X' < 48.9);
z = (48.9 - 52.5)/2.5
z = -1.44
From online p-value from z-score calculator, we have;
P(X' < 48.9) = 0.075 or 7.5%
B) For x' between 49 and 55, P(49 < X < 55)
At x' = 49;
z = (49 - 52.5)/2.5
z = -1.4
Z-score at x' = 55;
z = (55 - 52.5)/2.5
z = 1
From online p-value from z-score calculator, the p-value between the two z-scores is;
p = 0.7664 or 76.64%
Read more about z-scores at; https://brainly.com/question/6316394
Related Questions
HELP ME PLEASE......
Answers
Answer:
reflective.
Step-by-step explanation:
this has a somewhat meaningful undertone, meaning it is not sarcastic or scholarly. It also is not arguementative because it is not agrueing anything.
The question is down below.
AB=
Answers
Answer:
Step-by-step explanation:
This time we use the sin identity.
I am too lazy to write it out again but the answer is 6.97
HELP By Today
Please
The number of permutations of 5 objects taken 2 at a time is P(5,2). The value of
5!
P(5,2) could be found by applying 5P2=
(5 – 2)
What is the value of P(5,2)?
A-60
B-20
C-6
D-120
Answers
Answer:
20
Step-by-step explanation:
[tex](x + 2)(3x - ) = 0[/tex]
Answers
Answer:
∝∦⊄↑∫∫π≡³≥α㏑∩⊃∞
Step-by-step explanation:
Find the reference angle in radians: 7pi over 12
Answers
Answer:
5π/12
Step-by-step explanation:
5 pie / 12
(hope this helps can i plz have brainlist :D hehe)
PLEASE HELP!!! Needed asappp!
Answers
Step-by-step explanation:
Add the corresponding sides of the two equations
1.
2x=6
x=3
substitute for x
3+y=-1
y=-4
4.
5x=10
x=2
substitute for x
2(2)+2y=-2
2y=-6
y=-3
5.
12y=24
y=2
substitute for y
6x+5(2)=4
6x+10=4
x=-6
x=-1
Answer:
Q3. x = 3, y = -4
Q4. x = 2, y = -3
Q5. x = -1, y = 2
Step-by-step explanation:
Since the question is asking us to solve the system using elimination/adding, that's what I'll do.
To solve by adding, we add the like terms of both equations together.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1st question:
x + y = -1
x - y = 7
We add the first term together.
x + x = 2x
Then the second term.
y + -y = y - y = 0
Then the last term.
-1 + 7 = 6
Which becomes:
2x = 6
Then we solve the linear equation.
2x = 6
÷ 2 ÷ 2
x = 3
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
x + y = -1
Substitute x = 3
3 + y = -1
-3 -3
y = -4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2nd question:
2x + 2y = -2
3x - 2y = 12
We add the first term together.
2x + 3x = 5x
Then the second term.
2y + - 2y = 2y - 2y = 0
Then the last term.
-2 + 12 = 10
Which becomes:
5x = 10
Then we solve the linear equation.
5x = 10
÷5 ÷5
x = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
2x + 2y = -2
Substitute x = 2
4 + 2y = -2
-4 -4
2y = -6
÷2 ÷2
y = -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3rd question:
6x + 5y = 4
-6x + 7y = 20
We add the first term together.
6x + -6x = 6x - 6x = 0
Then the second term.
5y + 7y = 12y
Then the last term.
4 + 20 = 24
Which becomes:
12y = 24
Then we solve the linear equation.
12y = 24
÷12 ÷12
y = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
6x + 5y = 4
Substitute y = 2
6x + 10 = 4
-10 -10
6x = -6
÷6 ÷6
x = -1
x^3=27 what is the value of x?
Answers
Answer:
x = 3
Step-by-step explanation:
3*3*3 = 9*3 = 27
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex]x^3 =27[/tex]
Step 1: Take cube root.
[tex]x = (27)^(1/3)[/tex]
[tex]x=3[/tex]
Explanation in words (Short Form)
- Move the variable to the left and the other values to the right to determine the value of x. To ascertain the outcome, simplify the values.
- In this equation (x^3=27), we can solve this equation by taking the cube root and then ascertaining the outcome. The answer will result as x = 3 at the end for the following equation: x^3=27 to finding the value for x.
Answer:
[tex]x=3[/tex]
Hope this helps.
The vertex of a parabola is at the origin, and its focus is at . Which function does the graph with these attributes represent?
A.
B.
C.
D.
Answers
Answer:
ANSWER
step explanation:
The vertex of the parabola below is at the point (2,4), and the point (3,6) is on the parabola. What is the equation of the parabola? 10 (3,6) (2,4) TO 10 10 A. y= 2(x - 2)2 + 4 B. x = 4(y - 3)2 + 1 C. y= 6(x - 2)2 + 4 D. y = 3(x - 4)2 + 2
I WILL MARK BRAINLY HELP ME PLEASE! :)
Answers
Answer:
1. right
2. acute
3. obtuse
4. obtuse
5. acute
6. acute
7. scalene
8. scalene
9. isosceles
10. equilateral
11. scalene
12. isosceles
Step-by-step explanation:
What is the length,in meters,of VX?
Answers
Answer:
C) [tex]\sqrt{90}[/tex]
Step-by-step explanation:
VY = base and leg
XY = height and leg
VX = hypotenuse (c)
VY:
9 - 6 = 3
Solving for VX(c):
a² + b² = c²
3² + 9² = c²
9 + 81 = c²
c² = 90
c = [tex]\sqrt{90}[/tex]
Answer:The answer would be C 90
Step-by-step explanation:
NeverReady batteries has engineered a newer, longer-lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your statistics class questions this claim. You randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly,
Answers
Answer:
the probability is 0.0202
Step-by-step explanation:
The computation is shown below:
Given that
The Average life span = 17 hours
Standard deviation = 0.8 hours
Sample = 30 batteries
Sample mean = 16.7 hours
Now based on the above information
The probability is
[tex]P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202[/tex]
Hence, the probability is 0.0202
B.Exercise 1: Directions: Write TRUE if the given answer is correct and False if it is not, give the answer. ______1. Mary bought a magazine for Php 135.00, and 2 bottles of nail polish. Give an expression to represent the total amount she spent. Given answer: 2xp+135 or 2p + 135
Answers
Answer:
Verdader
o
Step-by-step explanation:
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 ft, width 18 ft, and depth 4 ft. Suppose water is pumped out of the
pool at a rate of 216 ft per hour. If the pool starts completely full, how many hours does it take to empty the pool?
hours ( NO LINKS , LINK WILL GET YOU BANNED )
Answers
Answer:
10 hours (I am not positive)
Step-by-step explanation:
We first want to find the volume of pool which is 30 x 18 x 4 = 2160.
Then you are going to divide by 216 to find how many hours it takes to drain the whole pool. (I'm not that big of an expert)
Need help on iready you get 13 points :)
Answers
Which is 40
4 times 2 is 8 8 time 5 is 40
Answer:
4 x 10
Step-by-step explanation:
4 x 2 x 5
4 x 2 = 8
8 x 5 = 40
4 x 10 = 40
Can y’all help me? I would really appreciate it
Answers
Answer:
I think the answer is she
A bowl is in the shape of a hemisphere. The radius of the bowl is 10 centimeters. How many liters of water can the bowl hold?
(1,000 cm = 1 liter)
Answers
Answer:
The bowl can hold 2.094 L.
Step-by-step explanation:
We want to find the volume of the hemisphere to calculate how many liters the bowl can hold. To find the volume of a hemisphere, we use this equation:
V = (2/3)•(π)•(r)³
Let's plug in what we know.
V = (2/3)(π)(10)³
Evaluate the exponent.
V = (2/3)(π)(1000)
Multiply.
V = 666.667π
V = 2094.395 cm³
Remember that 1000 cm = 1 liter, and we want to know how many liters the bowl can hold.
= 2094.395/1000
= 2.094 L
The bowl can hold 2.094 L.
Hope this helps!
Write an expression equivalent to
b10/b5
in the form bm.
Answers
Answer: M equals 7. So it would be b^7. When you multiply exponents you add them. When you divided them you subtract
Step-by-step explanation:
The equivalent expression will be b⁵.
What is an expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc.
Given an expression b¹⁰/b⁵,
We need to find an equivalent expression for the same,
So,
Using the identity,
mᵃ ÷ mᵇ = mᵃ ÷ mᵇ
= m⁽ᵃ⁻ᵇ⁾
Therefore,
b¹⁰/b⁵ = b⁽¹⁰⁻⁵⁾
= b⁵
Hence, the equivalent expression will be b⁵.
Learn more about expression click;
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) A different rectangle has area 12a² and perimeter 14a
What are the dimensions of this rectangle?
Dimensions:
. by
Answers
Answer:
l = 4a and b = 3a
Step-by-step explanation:
Given that,
The area of the rectangle, A = 12a²
Perimeter, P = 14a
The area and perimeter of a rectangle are given by :
A = lb
12a² = lb ....(1)
P = 2(l+b)
14a = 2(l+b) ....(2)
We need to solve equations (1) and (2). After solving we find that.
l = 4a and b = 3a
Hence, the dimensions of this rectangle are 4a and 3a.
A shoemaker claims his best product has an average lifespan of exactly 14 years. A skeptical customer asks for evidence (data) that might be used to evaluate this claim. The customer was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 6 years was calculated. Select the 95%, confidence interval for the true mean lifespan of this product.
Answers
Answer:
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0154
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0154\frac{6}{\sqrt{45}} = 1.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.8 = 13.2 years
The upper end of the interval is the sample mean added to M. So it is 15 + 1.8 = 16.8 years.
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.
6. What is the circumference of a circle at the right in terms of it
Answers
Answer:
The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle.
Step-by-step explanation:
FOR BRAINLIST!!
While building the White House model for the
iconic movie Independence day the movie makers
had to use a scale drawing in which the height of
the scale was 2 feet and the actual height of the
White house was 70 feet. If the actual length of the
white house is 168 feet, what is the length of the
scale model in feet?
А.
4.8 ft
B.
1.2 ft
5 ft
58.8 ft
Answers
Answer:
4.8
Step-by-step explanation:
Since the scale is 2 feet and the real is 70 to find the cale factor you do 70/2. Since the answer to that is 35 the scale factor is 35. SO to find tha drawing scale factor in feet you do 168/35 to get 4.8,
SolveABC where a = 11,6 = 13, &c = 15.
Answers
Answer: ABC = 2145
Step-by-step explanation:
11x13x15=2145
Answer:
whatever wawnser gimme brainliest
Choose all of the shapes that are used to create the net of a cylinder. circle triangle wedge rectangle
Answers
Answer:
trianglw
Step-by-step explanation:
Answer:
Two circles and a rectangle will make up a cylander.
Step-by-step explanation:
Have a good day! :)
Evaluate the following expression.
9 +62 – 2.8=
Answers
Answer: I think it’s 68.2
Answer:
68.2 for sure
Step-by-step explanation:
plz plz plz help me ill give brainliest i just really need help
Which rectangular prism has a surface area of 62 square units? [Note: Art is not drawn to scale.]
A rectangular prism with a length of 5, width of 3, and height of 1.
A rectangular prism with a length of 2, width of 2, and height of 6.
A rectangular prism with a length of 5, width of 3, and height of 2.
A rectangular prism with a length of 6, width of 2, and height of 4.
Answers
Answer:
C. when L =5, W = 3, H = 2
Step-by-step explanation:
2(wl + hl + hw)
2(15+5+3) = 46
2(4+12+12) = 56
2(15+10+6) = 62
Will the two expressions always be equivalent,
regardless of the value of p? Explain.
3(2p) and 2(3p)
Answers
Answer:
Yes
Step-by-step explanation:
If you multiply it out, the expressions have the same value of 6p, so whatever you plug in for p, it will always be the same
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other. How many different ways can they stand in line?
40 points && brainliest! pls help.
Answers
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other. So, there are 24 different ways they can stand in line.
How does factorial work?Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 till that considered integer.
Thus, if we want to take the factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other.
The different ways they can stand in line = 4!
[tex]= 4 \times 3 \times 2 \times 1\\\\= 12 \times 2\\\\24[/tex]
So, there are 24 different ways they can stand in line.
Learn more about factorials here:
https://brainly.com/question/16036678
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Write the equation in standard form. Y - 10= 2(x-8)
Answers
Answer:
2x-y=6
Step-by-step explanation:
y-10=2(x-8)
y-10=2x-16
-10+16=2x-y
6=2x-y or
standard form 2x-y=6
what is the slope for this graph ?
Answers
Answer:
um 6/1?
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The slope of a line is the change in the line. It is often referred to as the ([tex]\frac{rise}{run}[/tex]), the slope of the line can be found using the following formula,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
The graph of the given line gives one the points (7, 2), (9, 6). Substitute these points into the given formula and solve for the slope,
[tex]\frac{6 - 2}{9 - 7}[/tex]
Simplify,
[tex]=\frac{4}{2}[/tex]
[tex]=2[/tex]
I have 48 candys for 50cents each, how much total will I have after I sell all 48 candies?
Answers
Answer:
the answer is 2400 cents
Step-by-step explanation:
if you have 48 candies and each cost 50 cents so u meltiply 48 with 50. so if u mutiply them u get 2400cents, but if u want them in dollar then 1 dollar is 100 cent so if 1 dollar = 100 cent
? = 2400 cent
you criss -cross them so when u do 2400 multiplyed by 1 is 2400 and 100 multiplyed by ? is 100?
so your going to get this
2400 = 100?
so u divide both sides by 100 because u want "?" alone. so when u do 100 will vanish because you divided both sides with 100
so it will look something like this
2400/100 = ?
when u divide 2400 with 100 u get 24.
what does that mean? it mean 2400 cents are 24 dollars
do you get it?