Using the normal distribution, the probability is given as follows:
[tex]P(X \geq 10) = 0.0485[/tex].
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are:
p = 0.5, n = 13.
Hence the mean and the standard deviation are:
[tex]\mu = np = 13 \times 0.5 = 6.5[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{13 \times 0.5 \times 0.5} = 1.8028[/tex]Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, then:
[tex]P(X \geq 10) = 0.0485[/tex].
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1. An isosceles triangle has a base with a length of 14 inches and base angles that measure 68° each. Which
expression below correctly calculates the area of this isosceles triangle?
(1) 7²-tan (68°)
(2) 14²-sin (68°)
(3) 7²-cos (68°)
(4) 14-7-sin (68°)
None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).
To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.
However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.
We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.
tan(44°) = height/7, where 7 represents half of the base length.
Rearranging the equation, we have: height = 7 * tan(44°).
Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).
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Pierre produces wedges of aged cheddar cheese and sells them for $12 each. The table below shows the labor productivity
forPierre's cheese-making business. Fill in the missing values. Assume this is a perfectly competitive market.
Instructions: Round your answers to one decimal place.
Pierre's Cheese Business and Revenues
Labor
0
2
4
6
8
10
12
14
Total Product (wedges
of cheese)
(workers)
0
———
48
66
82
———
———
114
Marginal Product
(wedges of cheese)
/
12
——-
9
——-
7
5
4
Price
(dollars)
$12
12
12
12
12
12
12
12
Total Revenue
(dollars)
$0
288
———
792
984
———
1,272
———
Marginal Revenue
Product (dollars)
/
———
144
108
———
84
———
48
Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:
Marginal Product = Change in Total Product / Change in Labor
Marginal Revenue Product = Price x Marginal Product
Using the given information, we can fill in the missing values as follows:
Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product
0 0 - $12 $0 -
2 48 24 $12 $288 $288
4 66 9 $12 $792 $108
6 82 7 $12 $984 $84
8 96 5 $12 $1,152 $60
10 114 9 $12 $1,368 $108
12 132 9 $12 $1,584 $108
14 150 9 $12 $1,800 $108
So the missing values are:
Total Product for labor = 0 and 14: 0 and 150, respectively.
Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.
Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.
Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.
Step-by-step explanation: :)
Find the surface area and volume of the for fire. Round to the nearest tenth
The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A
How to determine the valuesThe formula for calculating the surface area of a cone is expressed as;
SA = πr² + πrl
Such that the parameters are;
r is the radius l is the lengthSubstitute the values, we have;
Surface area= 3.14 × 16 = 3.14 × 4 × 8
Multiply the values
Surface area = 50.24 + 100.48
Add the values
Surface area = 150.8 in²
Volume of the cone is;
Volume = 3.14 × 4² × 6.9/3
Volume = 3.14 × 16 × 6.9/3
Volume =116. 1in³
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Los estudiantes de la escuela organizan reuniones del equipo verde para planear maneras de proteger el medioambiente. Esta semana hay 144 miembros en la reunión, que es ek 90% del total del grupo
¿Cuál es el número total de miembros en el equipo verde?
If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.
If 144 members represent 90% of the total group, we can set up the equation:
144 = 0.9x
where x is the total number of members on the green team.
To solve for x, we can divide both sides of the equation by 0.9:
144 ÷ 0.9 = x
This simplifies to:
160 = x
To check our answer, we can verify that 144 is indeed 90% of 160:
144 ÷ 160 = 0.9
which confirms that our answer is correct.
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There is a multiple choice quiz with six questions and five possible answers and only one choice is correct what is the probability you get your first and only incorrect answer on the fourth question?n
Answer:1/1875
Step-by-step explanation:
the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.
The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:
(1/5) * (1/5) * (1/5) * (4/5) = 4/3125
Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.
8 cosθ-1=0 to the nearest 0.1°
Answer:
82.8°
Step-by-step explanation:
We can solve for θ by first isolating cosθ:
8 cosθ - 1 = 0
8 cosθ = 1
cosθ = 1/8
We can find the inverse cosine of 1/8:
θ = cos⁻¹(1/8) = 82.8191°
Rounding to the nearest 0.1°, we get:
θ ≈ 82.8°
What is the missing step in solving the inequality 4(x-3) + 4 ≤ 10+ 6x?
1. The distributive property: 4x-12 + 4 ≤ 10+ 6x
2. Combine like terms: 4x -8 ≤ 10+ 6x
3. The addition property of inequality: 4x ≤ 18 + 6x
4. The subtraction property of inequality: -2x ≤ 18
5. The division property of inequality:
O x≤-9
O x≥-9
0 x≤ - 1/2
0 x>-1
The value of inequality : x≤-9
Given,
Inequality 4(x-3) + 4 ≤ 10+ 6x
Firstly,
The distributive property: 4x-12 + 4 ≤ 10+ 6x
Then,
Combine like terms: 4x -8 ≤ 10+ 6x
Then,
The addition property of inequality: 4x ≤ 18 + 6x
Then,
The subtraction property of inequality: -2x ≤ 18
Then,
The division property of inequality:
Divide both sides of inequality by 2,
So,
x≤-9
Hence after last step the value of x is less than or equal to -9 .
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Solve and graph. |2x(x-1)+12|<=18
The solution of the inequality is -1 ≤ x ≤ 3.
To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:
2x(x-1) + 12 ≤ 18
-(2x(x-1) + 12) ≤ 18
Solving the first inequality:
2x(x-1) + 12 ≤ 18
2x² - 2x + 12 ≤ 18
2x² - 2x - 6 ≤ 0
Solving the second inequality:
-(2x(x-1) + 12) ≤ 18
-2x(x-1) - 12 ≤ 18
-2x² + 2x - 12 ≤ 18
2x² - 2x + 30 ≤ 0
Now, let's solve each inequality separately.
For the first inequality, 2x² - 2x - 6 ≤ 0:
We can factor this quadratic equation:
(2x + 2)(x - 3) ≤ 0
To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:
2x + 2 = 0 => x = -1
x - 3 = 0 => x = 3
Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.
For the second inequality, 2x² - 2x + 30 ≤ 0:
This quadratic equation does not have real solutions, so there are no solutions to this inequality.
Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.
To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.
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what is the probability of spinning a blue, then green
The probability of getting Blue then Green while spinning the wheel is
3 / 32
Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.
From the given figure we can find out the following information
The probability of getting Blue While spinning the wheel = 3/8
The probability of getting Green While spinning the Wheel = 2 / 8
The probability of getting Blue then Green while spinning the wheel
= 3/8 * 2/8
= 6/64
= 3/32
Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3 7/8, 5 1/4, 4, 6 1/8, 4 1/2, 5 1/4, 3 1/2, 5 3/8, 4 3/4, 5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be
able to plot all of the data above a label. Which should this fraction be?
A. tenths
B. eighths
C. fourths
D. halves
The required, the students use eighths as their scale, they will be able to plot all of the data points above the label. Option B is correct.
To make a line plot, the students will mark a number line with a scale that includes all the data points. Since the given data includes fractions with denominators of 2, 4, and 8, it would be best to choose a fraction that is a factor of all of these denominators. The only option that satisfies this condition is B. eighths.
To see why, note that 1/8 is a factor of 1/2 (4/8), 1/4 (2/8), and 1/8 (1/8). Therefore, if the students use eighths as their scale, they will be able to plot all of the data points above the label. Using any other fraction would require rounding some of the data points, which could lead to a loss of information.
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2. Find the amount of tax owed: commercial property valued at $340,000.00; assessed at 25%; taxed at $14.00 per hundred
dollars worth of property.
Answer:
55.0ml is answer = 22.05
Step-by-step explanation:
Use the table to add 199+61 vertically. The top row will be for regrouping (numbers that are "carried"). The bottom row will be for your answer. The addends have already been filled in for you.
The sum of the number 199 + 61 by vertical table will be 260.
Since, Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Use the table to add 199 + 61 vertically. Then we have
Hundreds Tens Ones
Regrouping 1 1
First addend 1 9 9
Second addend 0 6 1
Sum 2 6 0
Thus, The sum of the number 199 + 61 by the vertical table will be 260.
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The table to add 199+61 vertically is shown below.
To add 199 and 61 vertically, we'll set up the addition table as follows:
1 9 9
+ 6 1
_________
Let's start by adding the digits in the rightmost column, which is the ones place:
9 + 1 = 10
We write down 0 in the bottom row and carry over the 1 to the top row: 1 9 9
+ 6 1
_________
0
Now, let's add the digits in the next column (the tens place), including the carry-over:
1 + 9 + 1 = 11
We write down 1 in the bottom row and carry over the 1 to the top row:
1 9 9
+ 6 1
_________
1 1
Finally, let's add the digits in the leftmost column (the hundreds place), including the carry-over:
1 + 1 = 2
We write down 2 in the bottom row:
1 9 9
+ 6 1
_________
2 1
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Suppose that a safety deposit box at your bank costs $45/month to rent. How much would
it cost for you to rent the box for 15 years?
What are the first five terms of the sequence a_{n} = - 11 * (1/2) ^ (n - 1)
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
B) -11/2 - 11/4 - 11/16 - 11/32 - 11/8
C) -11, 5, - 9/4 - 4/3 - 7/8
D) -11, - 11/2 - 11/3 - 11/4 - 11/5
All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
We have to given that;
Rule for sequence is,
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Now, WE can find first five terms of sequence as;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Put n = 1;
⇒ a (1) = - 11 × (1/2)¹⁻¹
⇒ a (1) = - 11
Put n = 2;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (2) = - 11 × (1/2)²⁻¹
⇒ a (2) = - 11 × (1/2)¹
⇒ a (2) = - 11 / 2
Put n = 3;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (3) = - 11 × (1/2)³⁻¹
⇒ a (3) = - 11 × (1/4)
⇒ a (3) = - 11 / 4
Put n = 4;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (4) = - 11 × (1/2)⁴⁻¹
⇒ a (4) = - 11 × (1/2)³
⇒ a (4) = - 11 / 8
Put n = 5;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (5) = - 11 × (1/2)⁵⁻¹
⇒ a (5) = - 11 × (1/2)⁴
⇒ a (5) = - 11 / 16
Thus, All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
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In triunghiul ABC ,A este de 75 grade si B este de 45 grade. Daca AD perpendicular BC, D apartine BC si BE perpendicular AC, E apartine AC iar AB=12 Radical din 6 cm calculati lungimile AD si BE si Perimetrul ABC
Answer:
just start scamming
Step-by-step explanation:
HELPPP
Instructional Item I
A research group is trying to determine how many alligators are in a particular area. They
tagged 30 alligators and released them. Later, they counted 12 alligators who were tagged out
of the 150 they saw. What can the research group estimate is the total population of alligators
in that area?
Instructional Item 2
The local grocery store is going to donate milk and cookies to an upcoming middle school
event. They surveyed 150 students in the school to determine which type of milk they prefer
and recorded the results below.
Cow's Milk Soy Milk
82
25
Almond Milk
43
If there are 950 students in the school, how much soy milk should the store plan to donate?
The total population of alligators will be 375.
The amount of soy milk that the grocery store should plan to donate is: 158.
How to calculate the total population of alligators in the areaTo calculate the total population of alligators in the area, we will assign the following variables:
30 Tagged alligators = m
12 Counted alligators = k
150 alligators seen = n
The total population size (N bar) of alligators is calculated with the formula:
N bar = mn/k
= 30 * 150/12
= 4500/12
375
For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.
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A triangle has sides with lengths of 13 meters, 18 meters, and 8 meters. Is it a right triangle?
Answer:
The Pythagorean Theorem describes the relationship among the three sides of a right triangle
[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle
help me pleaseeeeeeeeeeeeeeee
Is the inverse of the function shown below also a
function? Explain your answer.
DONE ✔
AY
y
4
We can see here that it is true that the inverse of the function shown is also a function. This is true because the graph of the inverse of the function shown by reflecting the red graph about the line y = x.
What is a function?A function in mathematics is a unique connection between a group of inputs and their results. A function is a rule that specifically assigns one element from another set to each element in a set.
The set of inputs is referred to as the function's domain, while the set of outputs is referred to as the function's codomain.
From the given graph, we can deduce that the resulting graph is true for all x values and for all y values; it passes the vertical line test.
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A student scored 80% on a test. If the test had 50 questions worth one point each, how many questions did the student answer correctly?
Answer:
40
Step-by-step explanation:
All questions are worth the same, 1 point each.
80% of 50 = 0.8 × 50 = 40
Answer: 40
Answer:
40
Step-by-step explanation:
80/100*50 = 40
What is the value of x in the given triangle, in inches?
The numerical value of side length x in the right triangle is 8.
What is the numerical value of x?The figures in the image are two similar right triagles.
Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.
x/6 = (x + 4)/9
Cross multiply and solve for x:
6( x + 4 ) = x × 9
Apply distributive property:
6 × x + 6 × 4 = x × 9
Simplifying, we get:
6x + 24 = 9x
Subtract 6x from both sides:
6x - 6x + 24 = 9x - 6x
24 = 9x - 6x
24 = 3x
3x = 24
Divide both sides by 3:
x = 24/3
x = 8
Therefore, the value of 8.
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determine whether the function represents exponential growth or exponential decay
y=3(1.88)
Answer:
Exponential Growth
Step-by-step explanation:
The base of 1.88 is greater than 1, so there will be exponential growth
Directions: Transformations from the parent function y = x² are described
below. Write an equation to represent the function.
13, translated 2 units right
14. translated 5 units up
15. translated 3 units left and 4 units
down
17. reflected over the x-axis, then
translated 3 units down
16. translated 7 units right and 4
units up
18. reflected over the x-axis, then
translated 5 units right and 2 units
down
19. vertically compressed by a factor 20. vertically stretched by a factor
of 1/3, then translated 8 units up
of 2, reflected over the x-axis,
then translated 4 units left
The result of the transformation of the parent function y = x² are;
13. y = (x - 2)²
14. y = x² + 5
15. y = (x + 3)² - 4
16. y = (x - 7)² + 4
17. y = -(x²) - 3
18. y = -(x - 5)² - 2
19. y = (1/2)x²
20. y = (3x²) + 8
What are the results of the transformations?The transformations on the parent function y = x² can be described as;
13. Translated 2 units right:
The equation will be y = (x - 2)²
14. Translated 5 units up:
The equation will be y = x² + 5
15. Translated 3 units left and 4 units down:
The equation will be y = (x + 3)² - 4
16. Translated 7 units right and 4 units up:
The equation will be y = (x - 7)² + 4
17. Reflected over the x-axis, then translated 3 units down:
The equation will be y = -(x²) - 3
18. Reflected over the x-axis, then translated 5 units right and 2 units down:
The equation will be y = -(x - 5)² - 2
19. Vertically compressed by a factor of 2:
The equation will be y = (1/2)x²
20. Vertically stretched by a factor of 1/3, then translated 8 units up:
The equation will be y = (3x²) + 8
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A total of $48,000 is invested in two municipal bonds that pay 4.25% and 5.75% simple interest. The investor wants an annual interest income of $2400 from the investments. What amount should be invested in the 4.25% bond
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A basketball player guesses her team will score 54 points during the game. The player's team actually scores 60 points.
What is the percent error in the player's guess?
A: 5%
B: 10%
C: 12%
D: 15%
Answer:
6 divide by 60 into 100
Step-by-step explanation:
is 10
(05.03 MC)
A regular heptagon with 7 sides is inscribed in a circle with radius 8 millimeters. What is the area of
the figure? (3 points)
O 25.019 mm.2
O 150.112 mm.2
O 175.130 mm.²
205.639 mm.2
Answer:
i think 25.019mm2 is the correct answerrrrrrrr.
Answer:
175.130 mm^2
Step-by-step explanation:
Took the test.
Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?
A. 20
B. 26
C. 32
D. 36
How much less would Maria have to spend to have $70 per month available for saving?
A. $45.95
B. $75.95
C. $25.95
D. $24.05
Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.
Hence the correct option is (A).
From the given Maria's Income Statement we can see that,
Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.
Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36
So here net income = $ (630 - 98.36) = $ 531.64.
Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59
So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.
Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.
Hence the correct option will be (A).
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Use the Law of Sines to solve (if possible) the triangle: A = 25° 4', a = 9.5, b = 22? Round answer to two decimal places.
The measure of the angle B of the triangle is 78.15 degrees
How to determine the possible solutions from the triangleFrom the question, we have the following parameters that can be used in our computation:
A = 25 degrees
a = 9.5 units
b = 22 units
Using the law of sines, the angle B is calculated as
sin(A)/a = sin(B)/b
So, we have
sin(25)/9.5= sin(b)/22
This gives
sin(b) = 22 * sin(25)/9.5
Evaluate
sin(b) = 0.9787
Take the arc sin of both sides
b = 78.15
Hence, the measure of the angle is 78.15 degrees
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The length of timber cuts are normally distributed with a mean of 95 inches and a standard
deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the
mean of the sample will be between 94.7 inches and 95.3 inches?
O 0.998
O 0.436
O 0.002
O 0.950
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
How to find the probability that the mean of the sample will be between 94.7 inches and 95.3 inchesUsing the Central Limit Theorem.
The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.
Calculate the standard error of the mean (SEM):
SEM = σ / √n
SEM = 0.52 / √30
SEM ≈ 0.095
Calculate the z-scores for the lower and upper limits:
z1 = (94.7 - μ) / SEM
z2 = (95.3 - μ) / SEM
z1 = (94.7 - 95) / 0.095 ≈ -0.526
z2 = (95.3 - 95) / 0.095 ≈ 0.316
Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.
Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.
Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
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