The perimeter of 2nd right isosceles triangle is 16(√2 + 2).
If a is the equal sides of a right isosceles triangle,
Then its hypotenuse is √2 a and perimeter is √2a (√2 + 1 )
The perimeter of 1st right isosceles triangle is 16(√2 + 1)
= √2a (√2 + 1 )
= 16 (√2 + 1 )
a = 8√2
The hypotenuse of 1st triangle = √2 a
= √2 * 8√2
= 16cm
Let A be the equal sides of 2nd right isosceles triangle
Then its hypotenuse is √2 a and perimeter is √2a (√2 + 1 )
According to the question,
A = 16 cm
The perimeter of 2nd right isosceles triangle is √2 * 16(√2 + 1)
= 16(√2 + 2)
Hence, The perimeter of 2nd right isosceles triangle is 16(√2 + 2).
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use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.
The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.
Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588
As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.
Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.
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Find AD . CD = 5x-1 and AD = 4x+8
The numerical side length of length AD is 44 units
How to determine the length AD?From the question, we have the following lengths that can be used in our computation:
AD= 4x + 8
CD = 5x - 1
Also, from the complete question (added at the end of the solution), we understand that
The lengths AD and CD are congruent
These parameters and statements above mean that
AD = CD
Substitute the known values in the above equation, so, we have the following representation
4x + 8 = 5x - 1
Collect the like terms
5x - 4x = 1 + 8
Evaluate the like terms
x = 9
Substitute x = 9 in AD= 4x + 8
AD= 4 x 9 + 8
Evaluate
AD= 44
Hence, the length is 44 units
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Complete question
Given that lengths AD and CD are congruent.
Find AD
CD = 5x-1 and AD = 4x+8
how do the results compare to your hypothesis? explain why your hypothesis was/was not supported by the results?
Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.
Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.
Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
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3 times x plus 4 is no less than 4 times the sum of x and 1
There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:
3 Times x - Since there is an unknown variable (x), we can simply write the multiplication as 3x. "Plus 4" is also mentioned, so we write the first part as (3x + 4).No Less Than - This simply means "<". 4 Times the Sum of X and 1 - We can write this as 4(x + 1), considering we are adding an x variable to 1, however also multiplying. To organize this, we add parenthesis.
Hence, the final expression would be written as:
[tex](3x+4) < 4(x+1)[/tex]
Hope this helps!
Select the correct answer from each drop-down menu. Consider the following polynomials equations. A = 3 x 2 ( x − 1 ) B = − 3 x 3 + 4 x 2 − 2 x + 1 Perform each operation and determine if the result is a polynomial. Is the result of A + B a polynomial? Is the result of A - B a polynomial? Is the result of A · B a polynomial?
Carrying out the operations on the polynomials shows that
A + B - polynomial
A - B - polynomial
A * B - polynomial
How to determine the result of the operationsThe given polynomials are
A = 3x²( x − 1 )
B = -3x³ + 4x² − 2x + 1
A + B
= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² - 3x³ + 4x² − 2x + 1
= x² − 2x + 1
This is a polynomial
A - B
= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² + 3x³ - 4x² + 2x - 1
= 6x³ - 7x² + 2x - 1
This is a polynomial
A * B
= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)
= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)
= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²
= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²
This is a polynomial
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4. Identify each of the following polygons:
Answer:
H
Step-by-step explanation:
Work in attachment
any of y'all willing to do this? me on gram quietstorm703
read my comments
What is your question dude???????
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south carolina average? use
The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given:
Nationwide scores as n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3
Carolina scores as n2=500, [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3
So from here we can say
µ represents population mean.
[tex]u_{1}[/tex] represent population mean for nationwide scores.
[tex]u_{2}[/tex] represents population mean for Carolina scores.
[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given Question is incomplete, Complete Question here,
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?
use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.
State the hypotheses and identify the claim.
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Select the correct answer from each drop-down menu. Timothy purchased a computer for $1,000. The value of the computer depreciates by 20% every year. This situation represents. The rate of growth or decay, r, is equal to. So the value of the computer each year is % of the value in the previous year. It will take years for the value of the computer to reach $512.
It will take 3 years for the value of the computer of initial value $1000 to reach $512.
Given, Timothy purchased a computer for $1,000.
The value of the computer depreciates by 20% every year.
we have to find the number of years value of computer will take to reach $512.
Let, the function representing this situation be,
V(t) = AB^t
where, A is the initial value of the computer and B is the depreciating rate.
So, V(t) = (1000)(1 - 20/100)^t
V(t) = (1000)(0.8)^t
Now, the value will be, 512
512 = 1000(0.8)^t
0.512 = (0.8)^t
t = 3
So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.
Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.
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question content area top part 1 it is believed that gpa (grade point average, based on a four point scale) should have a positive linear relationship with act scores. attached below is the technology output for predicting gpa using act scores based on a data set of 8 randomly chosen students from a big-ten university. what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between gpa and act scores?
The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)
What is significance level?
"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.
The p-value for ACT is 0.0286
The significance level is 0.01 (1%)
Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.
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what is a general pattern in data
Answer:
rhe general pattern in data is........
Step-by-step explanation:
.....
the summary of the percent of times each and every category appears for the entire sample is called the:
The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .
In the question ,
it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,
it is called frequency distribution ,
Frequency distribution : it lists all categories of data and number of occurrences for each data category and
it is also the summary of percent of times each and every category appears for entire sample .
Therefore , the correct option is (d) .
The given question is incomplete , the complete question is
The summary of the percent of times each and every category appears for the entire sample is called the ,
(a) mode
(b) categorical percentage rate
(c) percentage distribution
(d) frequency distribution
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given the slope m of a line and a point (x, y) on that line, how can you determine the coordinates of another point on the line?
To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
The equation of the line is written in the slope-intercept form, which is:
y = mx + b, where m represents the slope and b represents the y-intercept.
Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.
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describe a procedure that could be used to write an equation having the first 7 natural numbers as solutions.
the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Now the simplest way to write an equation is to multiply all the factors.
The zeroes of the equation are 1,2,3,4,5,6,7.
The factors can be written as (x-1)* (x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7).
So the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
Hence, the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
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Solve the system algebraically.
4x+2y=104x+2y=10
x=y+13x=y+13
The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
4x + 2y = 10
x = y + 13
Now,
Since, The system of equations are,
⇒ 4x + 2y = 10 ..(i)
⇒ x = y + 13
⇒ x - y = 13 ..(ii)
Multiply by 2 in equation (ii) and add with (i);
⇒ 2x - 2y + 4x + 2y = 26 + 10
⇒ 6x = 36
⇒ x = 6
And, x - y = 13
⇒ 6 - y = 13
⇒ 6 - 13 = y
⇒ y = - 7
Thus, The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
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on the grid draw the graph of y= 1- 3x for values of x from -2 to 3
Answer:
see solution
Step-by-step explanation:
equation: y = 1 - 3x
when x is -2:
y = 1 -3 * -2 = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)
when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)
when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)
when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)
When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)
when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)
Plot these points on the graph and join up the dots to see the line.
bye
find two positive numbers that satisfy the given requirements. the sum of the first number squared and the second number is 51 and the product is a maximum. (first number) (second number)
The two positive numbers that satisfy the given requirements are √17 and 34
Given the sum of the first number squared and the second number
is 51.
Let's assume first number is x.
second number is y.
Square of first number is [tex]x^2[/tex].
sum of the first number squared and the second number = [tex]x^2 + y[/tex].
[tex]x^2 + y = 51[/tex]
subtract [tex]x^2[/tex] from both side of equal sign.
[tex]x^2 + y- x^2 = 51 - x^2[/tex]
[tex]y = 51 - x^2[/tex]
Product of both numbers p = x*y.
[tex]p = x*(51 - x^2)[/tex]
[tex]p = 51*x - x^3.[/tex]
Given the product is a maximum.
so derivative of p with respect to x will be = 0.
derivative of p with respect to x is [tex]51-3*x^2[/tex]
[tex]51-3*x^2 = 0[/tex]
[tex]3*x^2=51[/tex]
[tex]x^2 = 17[/tex]
x = √17.
put value of x in [tex]y = 51 - x^2[/tex]
[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34
So the value of x and y is √17 and 34 respectively.
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A professor wants to estimate how many hours per week her students study. A simple random sample of 65 students had a mean of 16 hours of studying per week. Construct a 98% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.4 hours per week. Round to two decimal places. Answer 2 Points Keypad Keyboard Shortcuts Lower Endpoint Upper Endpoint: Prev
98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
mean x = 16
standard deviation σ = 2.4
sample size n = 65
z score for 98% = 2.576
Interval = x±z*s/
= 16±2.576*2.4/
= 16±2.576*0.39629
= 16±1.0208
Interval = (21.0208,18.9792)
Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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Olaf has 11 more than triple the amount of customers as when he started selling newspapers. He now has 71
customers. Write an equation that can be used to solve for how many customers Olaf had originally, then solve
your equation to find the answer.
The equation representing the situation is written as
3x + 11 = 71the number of customers Olaf had originally is 80
How to write the equationFrom the given information the following is deduced
Olaf has 11 more than triple the amount of customers as when he started selling newspapers
let the amount be x
3x + 11 = ?
He now has 71 customers
3x + 11 = 71
solving the equation
3x = 71 - 11
3x = 60
x = 20
Olaf had 80 customers
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what is the rule for multiplying two integers that have the same sign
If multiplying 2 negative integers then it's a positive
If multiplying 2 positive integers it's positive
Answer: I hope this is helpful
Step-by-step explanation:
The proceeding pattern is summarized in the following rule for multiplying integers. Rule for Multiplying Two Integers: TO MULTIPLY INTEGERS WITH THE SAME SIGN, multiply the absolute value of the factors. The product is positive.
What is the value of x?
Enter your answer in the box.
Answer:
x=36
Step-by-step explanation:
At what point do the curves and intersect? find their angle of intersection correct to the nearest degree.
The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
What are angles?When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.
When two rays are linked at their ends, they create an angle in geometry.
The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.
Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
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A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
The change in rate of length of shadow is 2.692 ft/sec.
Given,
Height of tall person =7 ft
Height of tall lamp post = 20 ft
Rate at which tall person walks = 5 ft/sec
Let,
Distance between tall person and lamp post be x ft
the length of shadow be y ft
From similar triangles,
[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]
Differentiating on both sides with respect to time 't'
[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]
here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec
[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]
Thus, the change in rate of length of shadow is 2.692 ft/sec.
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Iris's checking account pays simple interest at 5% per year. She has $185 in
Answer:
Step-by-step explanation:
Answer 3700
Given the following probability distributions:
Distribution A Distribution B x p(x) x p(x)
0 .50 0 0.05
1 .20 1 0.10
2 .15 2 0.15
3 .10 3 0.20
4 .05 4 0.50
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.
Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).
a) Expected value for the distributions A and B is calculated as follows,
The expected value for distribution A,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]
The expected value for distribution B,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]
b) The standard deviation for the distributions A and B is calculated as follows,
First, find E(X²) for distribution A and B to substitute in the standard deviation formula.
The E(X²) for distribution A is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]
The E(X²) for distribution B is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]
Then, the standard deviation for distribution A is,
[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]
The standard deviation for distribution B is,
[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]
Distribution A and B have the same standard deviation.
c) The standard deviation values are the same for both distributions. But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.
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under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean?
When the population standard deviation is much greater than 5.
What is the standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, we have
The circumstance is a score that is 5 points above the mean considered a central value.
We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.
We concluded from the above statement that when the population standard deviation is much greater than 5.
Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.
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A certain type of mango that weighs over 425 grams is considered to be large in size. the weights for this type of mango, x grams, are normally distributed with a mean of 400 and a standard deviation of 25. find the probability that a randomly selected mango of this type will not be considered as large size. round your answer to four decimal places.
The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.
Explain the term z-distribution/normal distribution?The statistics field is where z-distribution probability is most frequently employed. It is used to determine a person's height, weight, and pay. The graph produced by these measurements is symmetrical.For the stated question;
The formula for the z-score is;
z = (x - μ)/σ
x < 425 gram
mean μ = 400,
standard deviation σ = 40:
Thus,
z = (425 - 400)/40
z = 0.625
P(X < 425) = 1 - P(z = 0.625)
P(X < 425) = 1 - 0.7357
P(X < 425) = 0.2643
Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.
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Answer:0.8413
Step-by-step explanation:
0.8413
The mean is μ=400, and the standard deviation is σ=25.
Open Excel. Click on an empty cell. Type =NORMDIST(425,400,25,1) and press ENTER.
The probability, rounded to four decimal places, is P(X<425)≈0.8413.
you want to estimate the mean sat score of all georgia students. you know the mean score for a random sample of georgia students is 1050. what number is your best guess as to the mean score for all georgia students?
The best guess for the mean score for all the Georgia students would be 1050 number here.
Given that:
The mean score for a random sample of Georgia students is 1050.
Assuming,
1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.
1) The standard error is computed as:
[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]
2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.
2) The Z-value is computed as:
[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]
3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.
3) The Z -score here is computed as:
[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]
The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.
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d • r = r • d what is the property
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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