Answer:
9⁶
Step-by-step explanation:
[tex]\dfrac{9^2}{9^{-4}} = 9^2 9^{4} = 9 ^ {(2 + 4)} = 9^6[/tex]
Reciprocal of a number raised to exponent is the same as the number raised to the negative of the original exponent
So
[tex]\dfrac{1}{9^{-4}} \text{ becomes } 9^4[/tex]
At one university, the mean distance commuted to campus by students is 19.0 miles, with a standard deviation of 4.2 miles. Suppose that the commute distances are normally distributed. Complete the following statements. (a) Approximately 95% of the students have commute distances between miles and miles. (b) Approximately 7 miles and 31.6 miles. of the students have commute distances between 6.4
The average commute for 95% of the students is between 19.0 and 4.2 miles.
The average distance is 19 miles.
Therefore, the standard deviation is 4.2 miles.
A) 2.7 = 19 - a(4.2)
where;
a deviates from the mean by a certain number of standard deviations. Thus;
a = (19 - 2.7) ÷ 4.2
a = 3
In a normal distribution, 3 standard deviations from the mean indicate that 95% of the data falls within that range.
B) The data are 2 standard deviations apart from the mean at the 95% confidence level. Thus;
CI = 19 ± 2(4.2)
CI = (18 - 10.2) OR (18 + 10.2)
CI = (7.8, 28.2)
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Write the statement "the sum of a number and 18.4 is at least −3.8" as an inequality.
−3.8 + b > 18.4
b + 18.4 ≥ −3.8
b + 18.4 ≤ −3.8
−3.8 + b < 18.4
Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
The sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality.
Let [tex]b[/tex] be the number
As it is mentioned that the sum of [tex]x[/tex] and [tex]18.4[/tex] is at least [tex]-3.8[/tex].
Hence, the sum is greater or equal to [tex]-3.8[/tex]
i.e., [tex](b+18.4)\geq -3.8[/tex]
Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].
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PLEASE ANSWER ASAP
Which statement correctly describe the data shown in the scatter plot?
Responses
The scatter plot shows no association.
The scatter plot shows no association.
The scatter plot shows a linear association.
The scatter plot shows a linear association.
The point (2, 14) is an outlier.
The point , left parenthesis 2 comma 14 right parenthesis, is an outlier.
The scatter plot shows a negative association.
"The scatter plot shows a linear association."
What is scatter plot ?
Several dots are plotted on horizontal and vertical axes to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).
But how? Well, linear means: "arranged in or extending along a straight or nearly straight line." Which if you didn't notice.. All the points on the graph, make up a generally straight line.
"No association" means there is no line or association with any of the points. So, you'd pick that if the points were all over the graph in no order, line or combination; which isn't the case.
"Negative association" is when the top of the points come from the left of the graph lowering into the right. While Positive association would be from right to left. So, it couldn't be choice "Negative Association" since it's coming from right to the left of the graph.
"The point (2, 14) is an outlier." If you didn't know, an outlier is one dot out of a whole group. Think of it as if EVERYONE was wearing pink except one; who wore black. It's just the out of placed kind of dot; but it's supposed to be there. When you look at the graph, there is no dot or outlier at point (2,14) so, that's automatically out as well.
Ending with the last choice "The scatter plot shows a linear association." which is not just true but is the only one that'd make since.
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Hello can someone help me with this question please
The exponential equation that models the population of the bacteria is:
y = 5*(7)^x
How to write the exponential equation?The general exponential equation is of the form:
y = A*(b)^x
Where A is the initial value, b is the base, and x is the variable.
Initially, Zach counted 5 bacteria, then:
A = 5
And we know that after one hour, Zach saw 35 bacteria, then we can write the equation:
35 = 5*(b)^1
35 = 5*b
35/5 =b
7 = b
Then the exponential equation is:
y = 5*(7)^x
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Given the equation, y=3x, complete the table of values
x (input)
y (output)
-2
-1
0
1
2
Answer:
-2, -6
-1, -3
0,0
1,3
2,6
Step-by-step explanation:
nsd fbvdvjben ebtv
Step-by-step explanation:
when x is -2 y is y=3x
y=3×-2
y=-6 do that for all
5. in a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3. how many pounds of raisins will there be in 7 pounds of this mixture?
The pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
It is given that:
In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3
Let the common factor be x:
7x = raising
3x = dates
7x + 3x = 7
10x = 7
x = 7/10
7x = 7(7/10)
Raisin = 49/10 pounds
Thus, the pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.
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A department store buys 200 shirts at a cost of $1400 and sells them at a selling price of $10 each. Find the percent markup.
The percent markup price is equivalent to 42.86%.
What is a expression? What is a mathematical equation? What is Equation Modelling?
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a department store buys 200 shirts at a cost of $1400 and sells them at a selling price of $10 each
Cost price of 200 shirts = C.P. = $1400
Selling price of 200 shirts = S.P = $(10 x 200) = $2000
Percentage markup = [(2000 - 1400)/1400] x 100 = (600/1400) x 100 = 600/14 = 42.86%.
Therefore, the percent markup price is equivalent to 42.86%.
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Answer: the answer would round up to 43
Step-by-step explanation:
What is the smallest value or
lower extreme?
A. 304
B. 100
C. 400
Answer:
B. 100
Step-by-step explanation:
The lower extreme is the number in line with the left most dot.
What is the result when the number 8 is decreased by 25%?
Answer:
6
Step-by-step explanation:
8 * (1.0 - .25) = 6
Answer: 6
Step-by-step explanation: 8 - 4 is equivalent to 8 - 50%, cut 4 in half which gives 2, 2 is 25% of 8, so 8 - 2 = 6
A class has 20 women and 16 men. In how many ways can you (a) put all the students in a row? (b) put 7 of the students in a row? (c) put all the students in a row if all the women are on the left and all the men are on the right?
Part a: All the students in a row = 36!.
Part b: 7 of the students in a row; 36 x 35 x 34 x 33 x 32 x 31 x 30.
Part c: women on the left = 20! x 16!
Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the orientation of the selection is irrelevant. You can choose the component of combos in any order. Permutations and combinations can be jumbled up.For the stated question-
The class contains-
20 women16 menTotal students = 36Part a: all the students in a row.
Number of ways = 36!
Part b: 7 of the students in a row.
Number of ways = 36 x 35 x 34 x 33 x 32 x 31 x 30
Part c: All the students in a row if all the women are on the left and all the men are on the right.
women on the left = 20! x 16!
Thus, the number of ways in which all the students in a row if all the women are on the left and all the men are on the right is; 20! x 16!.
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the percentage of children ages 1 to 14 living in poverty in 1985 compared to 1991 for 12 states was gathered. part a: determine and interpret the lsrl. (3 points) part b: predict the percentage of children living in poverty in 1991 for state 13 if the percentage in 1985 was 19.5. show your work. (3 points) part c: calculate and interpret the residual for state 13 if the observed percent of poverty in 1991 was 22.7. show your work. (4 points)
Answer:
Part A: The LSRL is y^ = 7.76 + 0.6x.
Part B: y^ = 7.76 + 0.6(19.5) = 19.46
y^ = 19.46%
Part C: 22.7 - 19.46 = 3.24. The residual is 3.24. This means that the value was underpredicted.
Step-by-step explanation:
A researcher wishes to calculate the height of patients suffering from a heart disease. From patient records, the mean was computed to be 156cm, with a standard deviation of 5cm. Further investigation reveals that the scale was misaligned, and that all readings are 2cm too large, for example, a patient whose height is really 180cm was measured as 182 cm. Furthermore, the researcher would like to work with statistics based on meters (1 meter= 100 centimeters). What would be the revised values for the mean and standard deviation of the patients’ height?
The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm
What is the mean and standard deviation?Let us assume that the number of Patients is denoted as P. We are given;
Mean = 156 cm
We know that mean here is gotten from the formula;
Mean = Total height/number of patients
Thus;
Total Height = 156P cm
We are told that each height was measured 2 cm more. Thus;
Total height reduction = 2P cm
Thus;
Actual Total Height = 156P - 2P = 154P cm
Mean = 154P/P = 154 cm
Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm
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Convert y-8.25=(x-3) into slope intercept form
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = (x - 3)
y - 8.25 = x - 3
y = x + 5.25
Could you please give me brainliest for this? Thank you!
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = x - 3 Add 8.25 to both sides of the equation
y = x + 5.25
Members of a lacrosse team raised $1581. 75 to go to a tournament. They rented a bus for $968. 50 and budgeted $55. 75 per player for meals. Write and solve an equation which can be used to determine pp, the number of players the team can bring to the tournament.
The equation to determine the number of players is (x-y)/z and there are 11 players in total.
What does a math equation mean?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.Given: Lacrosse players raised $1581.75 to attend a tournament. They allocated $968.50 for the bus rental and $55.75 for each player's meals.
Let,
x = amount raised to attend a tournament.
y = amount allocated for bus rental
z = amount for each player's meals
Number of players = (x-y)/z
= (1581.75-968.50)/55.75
= 613.25/55.75
= 11
Therefore, the equation to determine the number of players is (x-y)/z and there are 11 players in total.
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focus on the means (mean). - what do you notice about the means of the sample means as the sample size increases from 1 to 100? - what would you expect the mean of the sample means to equal if n
As the sample size increases the mean is 100 , if n = 1000 , the mean of the sample means will be unchanged .
In the question ,
from the table we can observe that ,
if n = 1 , the mean is 97.656 ,
if n = 5 , the mean is 100.101 ,
if n = 10 , the mean is 100.006 ,
if n = 100 , the mean is 100.341 ,
from the table we notice that as the sample size increases from 1 to 100 , the means of the sample means are same that is 100 .
we can see that for every n , the mean is approximately equal to 100 ,
So , if n = 1000 , then the mean will also be approximately equal to 100 .
Therefore , the mean of the sample means will be unchanged .
The given question is incomplete , the complete question is
Focus on the means. What do you notice about the means of the sample means as the sample size increases from 1 to 100? What would you expect the mean of the sample means to equal if n = 1000 ?
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If a line has a slope of 8 and includes the points (9, u) and (10, –1). What is the value of u?
The value of u that completes the ordered pairs is -9
How to calculate the value of u?From the question, the points are given as
(9, u) and (10, -1)
Slope = 8
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (9, u) and (10, -1)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (9, u) and (10, -1)
Substitute the known values in the above equation
So, we have the following equation
8 = (u + 1)/(9 - 10)
Evaluate
u + 1 = -8
So, we have
u = -9
Hence, the value of u is -9
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4. A room is 10 ft by 12 ft. How many square yards are in the room?
The area of the room is 120 ft² (area = length x width).
The room is 10 ft by 12 ft
The area of the room = 120 sq ft
1 yard= 3 feet
1 square yard=9 sq feet
The area of the room = 120 sq ft or 120/9=13.33 sq yards
Answer: 13.33 sq yards
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.
a) The expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3. b) The value of standard deviation of two distributions is same. c) A is less than the expected value for the distribution B.
The calculation for expected value of distribution of A is given as,
E(X) = ∑[tex]^{n}[/tex][tex]_{i=1}[/tex]= [tex]X_{i}[/tex]. P (X=x)
=0⋅ (0.50 )+1⋅(0.20)+....+4⋅0.05=1
E(X) = ∑i=1nXi.P(X=x)=0⋅(0.50)+1⋅(0.20)+....+4⋅(0.05)=1
The calculation for expected value of distribution of B is given as,
E(X)=n∑i=1 Xi.P(X=x)
=0⋅(0.05)+1⋅(0.1)+....+4⋅(0.50)=3
E(X)=∑i=1nXi.P(X=x)=0⋅(0.05)+1⋅(0.10)+....+4⋅(0.50)
=3
Therefore, the expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3.
(b) The formula for standard deviation is given as,
σ=√E(X2)−E(X))2
The calculation for the E(X2) of distribution A is given as,
E(X2)=n∑i=1 X2i⋅P(X=x)
=02⋅(0.50)+12⋅(0.20)2+.....+42⋅(0.05)=2.5
The calculation for the E(X2) of distribution B is given as,
E(X2)=n∑i=1 X2i⋅P(X=x)
=02⋅ 0.05)+12⋅(0.10)+......+42⋅(0.50)
=10.5
E(X2)=∑i=1nXi2⋅P(X=x)=02⋅(0.05)+12⋅(0.10)2+......+42⋅(0.50)
=10.5
The value of standard deviation for the distribution A is given as,
σA=√2.5−12
=1.225
The value of standard deviation for the distribution B is given as,
σB=√10.5−32
= 1.225
Therefore, the value of standard deviation of two distributions is same.
(c) The expected value for distribution A is less than the expected value for the distribution B. The standard deviation is same for both distributions; the spread between both the distributions is same. Therefore, the distribution B is better than distribution A.
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problem 1. monthly sales are independent normal random variables with mean 120 and standard deviation 5. (a) find the probability that exactly 4 of the next 6 months have sales greater than 120. (b) find the probability that the total of the sales in the next 4 months is greater than 500.
Probability - The answer to the problem is P(Y = 4) = 3/32
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Solution:
Mean = 120
Standard Deviation = 5
Z = (X - Mean)/Standard Deviation
Z = 1/2
(i) P(Y = 4) = 6/4 * (1/2)^2 * (1-1/2)^6-4
P(Y = 4) = 3/2 * 1/4 * 1/4
P(Y = 4) = 3/32
(ii)P(X > 500) = 1 - P(X ≤ 500)
= 1 - Φ(500; 480, 10)
= 1 - 0.9772
= 0.0228
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Solve.
−5/6 = − 1/4 − 7/10 x
Enter your answer as a fraction in simplest form in the box.
x =
Answer:
-5/6=-1/4-7/10 x /×60
60×(-5/6)=60×(-1/4)+60(-7/10 x)
-50=-15-42 x
-50+15=-42 x
-35=-42 x
35=42 x
x=35/42
x=5/6
PLEASE HURY IM TIMED!!!!!!!
pick true or false.
Inequality True False
6.1<6.1
−2≤−2
5.6≥5.6
-4 > 4
Answer:
Step-by-step explanation:
false true true false
Answer:
false true true and false
Step-by-step explanation:
what is the probability that headway is within 1 standard deviation of the mean value? (round your answer to three decimal places.)
The probability that headway is within 1 standard deviation of the mean value is 0.890.
What is mean value?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.
Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).
The cdf for the distribution is
[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]
Now calculate the value of F(1.445) and F(0.995).
F(1.445) = 1 - (1/(1.445)⁶)
F(0.995) = 0
Now putting the value of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):
P( 0.995 ≤ x ≤ 1.445)
=1 - (1/(1.445)⁶) - 0
=0.890
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what is the estimate of 26% of 78
26% of 78
= 26*(1/100)*78
=(26/100)*78
=0.26*78 = 20.28
so, the required answer is 20.28.
what is percentage?
answer: The quantity of something represented as if it were a portion of a sum total of 100; a portion or share of a whole.
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You roll two dice, one red and one green. Losing combinations are doubles (both dice showing the same number) and outcomes in which the green die shows an odd number and the red die shows an even number. The other combinations are winning ones. E is the event that you roll a winning combination.
The likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.
Here,
If the first die is red and the second one is green, then the sample space S is the following:
S=
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)
Hence n(S)=36.
Let's list the losing combinations:
E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),
(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}
n(E)=15
There are 36 total possiblities.
Out of which, winning probability is 21.
=21/36
=7/12
Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.
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A pharmacist asserts that more than 40% of prescribed medicines are derived from plants. They decide to test this assertion by computing the sample proportion for a random sample. The data results in a test statistic of z = 2.14 and a P- value of .0162. Test at a 5% significance level. a. State the hypotheses for their test. b. Briefly describe what the P-value is. c. Using the test statistic, how was the P-value found? d. Based on the P-value what conclusion should the pharmacist make? In particular, do they have enough evidence in support of their claim?
a. test statistic = 1.35
p-value = 0.198439
b. Support the null hypothesis.
So you have the hypothesis:
H₀:μ=4
H₁:μ≠4
with the sample information you calculate the statistic using the t-distribution with 14 (n-1) degrees of freedom:
t=x[bar] - μ ⇒ t= 4.8 - 4 = 0.8 = 1.347≅ 1.35
s/√n 2.3/√15 0.59
The p-value is defined as the probability corresponding to the calculated statistic (or of obtaining a value as extreme as the value of the statistic) if possible under the null hypothesis.
p-value: 0.198439
b.
Since the calculated p-value is greater than the significance level, you don't reject the null hypothesis.
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which relationships describe angles 1 and 2? select each correct answer. responses complementary angles complementary angles adjacent angles adjacent angles vertical angles vertical angles supplementary angles supplementary angles a line goes left to right with a ray in the middle creating a right angle and another ray between the right angle with a one labeling the left angle and a two labeling the right angle
Angles 1 and 2 are neighboring, hence the fourth choice is accurate. Angles 1 and 2 are adjacent.
The term "Angle" refers to the separation between line segments or rays that converge at a single point.
The following may be said about angles 1 & 2:
In a line that proceeds from left to right, there is a ray in the middle that forms a right angle, a second ray between the two right angles, and one light that labels both the left angle and the right angle.
We can draw just as in the image.
Angles 1 and 2 are neighboring because they share a vertex, as seen in the image.
Angle 2 equals 90 degrees
Angle 1 equals 45 degrees
Angles 1 and 2 are adjacent, so option 4 is correct because it describes the relationship between them.
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HELP ME ASAP What is the best estimate of the solution to the system?
Answer:
(-3.4,2.7)
Step-by-step explanation:
The reason it's asking for an estimate, is because the intersection point is not on exact integer coordinates.
Start with the x-value of the intersection point. All options contain either -3.4 or -3.7. The x-value of the intersection point is closer to -3 than -4, so -3.4 is a better estimate.
Do the same with the y-value. Since the intersection point is closer to 3 than 2, 2.7 is the best estimate here.
Answer:
Last choice: (-3.4, 2.7)
Step-by-step explanation:
Well, you could actually solve the two line equations and arrive at the answer but that is not the intent of the question.
The solution of the two line equations is the point at which the two lines intersect
At this point the x value is closer to -3 than to -4. So the x value from the choices would be -3.4 rather than -3.7
We can eliminate 1st and 3rd choices
The y value is closer to 3 than it is to 2 so the y-value estimate would be 2.7
Correct choice: (-3.4, 2.7)
I have marked the solution point with an X in the attached image
Pentagon PQRST is a scale drawing of pentagon ABCDE.
In the scale drawing of the 2 pentagons the value of x is 3
How to find the value of xTo find the value of x in the pentagon, the scale factor is first determined
The scale factor is solved for as follows
AB * r = PQ
in the figure AB = 5 and PQ =2.5
5r = 2.5
r = 2.5 / 5
r = 0.5
Using the scale factor r = 0.5
6 * r = x
6 * 0.5 = x
3 = x
x = 3
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assume that x and y are independent. what are the expected value and the standard deviation of the points per game for the player?
The expected value and the standard deviation of the points per game for the player is -6.5 and 65.43 respectively.
Given:
In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played.
From the given table:
E ( X ) = 9.5 * 5 points
= 47.5
E ( Y ) = 5.4 * - 10
= -54
E ( X + Y ) = 47.5 + ( -54 )
= 47.5 - 54
= -6.5
SD ( X ) = 12.5 * 5
= 64.5
SD ( Y ) = - 11
SD ( X + Y ) = [tex]\sqrt{64.5^2 + (-11)^2}[/tex]
= 65.43
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Full question:
Is in the image uploaded.
In an all boys school, the heights of the student body are normally distributed with a mean of 68 inches and a standard deviation of 4. 5 inches. Using the empirical rule, what percentage of the boys are between 54. 5 and 81. 5 inches tall?.
According to the empirical law of statistics, 99.7% of the males are between 54.5" and 81.5" tall.
What is empirical rule?The 68-95-99.7 rule, also known as the empirical rule, indicates where most of the values in a normal distribution are distributed: The majority of values—about 68%—fall within the range of the mean. The average value is within two standard deviations for about 95% of the data. Almost all values, 99.7% of them, fall within a 3 standard deviation range.
Here,
mean=68 inch
standard deviation=4.5 inch
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
68−4.5=63.5
68+4.5=72.5
The range of numbers is 63.5 to 72.5
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
68−2⋅4.5=59
68+2⋅4.5=77
The range of numbers is 59 to 77
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
68−3⋅4.5=54.5
68+3⋅4.5=81.5
The range of numbers is 54.5 to 81.5
99.7% of the boys are between 54. 5 and 81. 5 inches tall using the empirical rule of statistics.
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