Use normal approximation to estimate the probability of getting more than 52 girls in 100 births. Assume that boys and girls are equally likely.
Answers
The probability of getting more than 52 girls in 100 births is 0.3446
This is further explained below.
What is the probability?Generally, The ratio of females to boys per one hundred births is modeled here as:
[tex]\large X \sim Bin(n = 100, p = 0.5)[/tex]
Where
Bin shows binomial
n=sample size
p=sample proportion
The following is an approximation of this using the normal distribution:
[tex]\large X \sim N(\mu= np, \sigma^2 = np(1-p))\\\\\large X \sim N(\mu= 100*0.5 , \sigma^2 = 100*0.5*0.5)\\\\\large X \sim N(\mu= 50 , \sigma^2 = 25)\\\\\large X \sim N(\mu= 50 , \sigma = 5)[/tex]
In light of this, the formula for calculating the probability is as follows:
P(X > 52)
When we take into account the continuity correction factor, we obtain the following:
P(X > 52.5)
After transforming it into a regular variable according to the standards, the following is what we get:
P(Z > (52.5 - 50) / 5)
= P(Z > 0.5)
Taking this information from the usual normal tables, we get the following:
P(Z > 0.5) = 0.3085
in conclusion, the necessary probability in this scenario is 0.3085. It should be noted that we may do this without correcting the continuity, in which case:
P(X > 52)
[tex]= P(Z > (\frac{52 - 50}{ 5})[/tex]
= P(Z > 0.4)
= 0.3446
Hence, the necessary probability in this scenario is 0.3446.
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Related Questions
DIVIDE THE POLYNOMIALS USING LONG METHOD. QUESTION 1 Divide (x4 + 2x³ - 13x² - 38x - 24) + (x + 4)
Answers
Answer:
QUESTION 1: x³ - 2 x² - 5 x - 18 remainder 48
Find 3 consecutive numbers whose sum is 132
Answers
Answer:
Integer 1- 43
Integer 2- 44
Integer 3- 45
Step-by-step explanation:
x+(x+1)+ (x+2)=132
3x+3-3=132-3
3x=127
/3 /3
x=43
x+1=44
x+2=45
141% as a mixed or whole number
Answers
Answer:
1 41/100
Step-by-step explanation:
Answer:
141/100 (Already in simplest form). As a mixed number, it is: 1 41/100
Step-by-step explanation:
What is the y intercept of the function shown?
Answers
Answer:
-2
Step-by-step explanation:
The line passes through the y-intercept at the point (0, -2)
Please see attached question
Answers
The probability that the student is a sixth-grader or rated good grades as most important is (168 / 335) + (135 / 335) = 0.904
What is the probability?Probability is used to determine the odds that a random event would happen. The odds that the event would happen lies between 0 and 1.
The probability that the student is a sixth-grader or rated good grades as most important = (number of sixth-graders / total number of students) + (students who rates good grades as most important / total number of students)
(168 / 335) + (135 / 335) = 303 / 335 = 0.904
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A model rocket reaches a maximum height of 2000 feet above ground and begins to
descend at a rate of 75 feet per second. Which equation models the height above
ground, y, of the model rocket, x seconds after it reaches its maximum height?
Answers
The equation which is best representing the height above ground, y, of the model rocket and x seconds after it reaches the maximum height is 75x + y = 2000.
The height above ground, y, of the model rocket, x seconds after it reaches its maximum height can be represent by a linear equation,
The maximum height is 2000 feet, after this the rocket starts to descend with a rate of 75 feet per second.
Let us say that when the rocket starts descending, our time is started from zero,
So, on plotting these points of graph, we can one point, (0,2000).
The rate of descend is the slope m of the graph,
m = -75 ft/s
We are taking it negative because height is decreasing with time,
We can use the point slope form of equation of line,
It says, if a line passes through (a,b) and has slope m. Then the equation of line is,
(y-b) = m(x-a)
So, our line is passing through (0,2000) and has slope -75 ft/s.
So, equation of the line is,
(y-2000) = -75(x-0)
75x + y = 2000.
This above equation of line is representing the relation between the height above ground and time of the model rocket.
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What is the slope of the line that passes through the points (-4, -10)) and (-7, -19)
? Write your answer in simplest form.
Answers
Answer:
Slope = 3
Step-by-step explanation:
(-4, -10) and (-7, -19)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -19 - (-10) -19 + 10 -9
m = ------------ = ---------------- = ------------- = -------- = 3
x₂ - x₁ -7 - (-4) -7 + 4 -3
I hope this helps!
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}[/tex]
I need to know how to rewrite the expression using the distributive property of multiplication over addition
Answers
Given the following expression:
[tex]\text{ 10(3 + 2)}[/tex]Rewriting this using the distributive property of multiplication over addition will be:
[tex]\text{ 10(3) + 10(2)}[/tex]Therefore, the answer is letter B - 10(3) + 10(2)
Solve for U.
-3 + 2u + 6 = -8u - 7
What does U equal?
Answers
Answer:
U = -1
Step-by-step explanation:
Answer:
u=-1
Step-by-step explanation:
-3 + 2u + 6 = -8u - 7
2u-3+6=-8u-7
2u+3=-8u-7
we will collect like terms
2u+8u=-7-3
10u=-10
u=-1
rate as brainliest
Evaluate. Write your answer as a whole number or as a simplified fraction.
4^-2 / 6^3
Answers
Answer:
Your answer is [tex]\frac{1}{864}[/tex]
Step-by-step explanation:
[tex]4^{-1}[/tex] ÷ [tex]6^{3}[/tex] [tex]= 0.0011574074[/tex] or [tex]\frac{1}{864}[/tex]
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 millimeters, and a variance of 64.
If 416 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than
0.65 millimeters? Round your answer to four decimal places.
Answers
If g :R → R is given by g(x) = x2 + 3 , find the function f such that (g. f) (x) = 4x2 + 3. A. 3x B. 4x C. 2x D. None of these
Answers
Given:
[tex]\begin{gathered} g(x)=x^2+3_{} \\ (g\circ f)(x)=4x^2+3 \end{gathered}[/tex][tex](g\circ f)(x)=g(f(x)[/tex]Let substitute one by one from the given options.
[tex]\begin{gathered} g(3x)=(3x)^2+3 \\ g(3x)=9x^2+3 \end{gathered}[/tex]3x is not the function f.
[tex]\begin{gathered} g(4x)=(4x)^2+3 \\ g(4x)=16x^2+3 \end{gathered}[/tex]4x is not the function f.
[tex]\begin{gathered} g(2x)=(2x)^2+3 \\ g(2x)=4x^2+3 \end{gathered}[/tex]2x is the function f.
[tex]f(x)=2x[/tex]Option C is the final answer.
Question 5 (05.05)Based on the graph, what is the initial value of the linear relationship?
Answers
4
1) Examining that graph, we can see that this is a decreasing function, due to the line direction. And that the initial value is the y-intercept.
2) Hence, the initial value is 4. Notice that all values after that goes decreasing for y.
Please help!
6|x - 8| ≤ 12
x ≤ ?
x ≤ ?
Answers
Answer: 10, 6
Step-by-step explanation:
[tex]6|x-8| \leq 12\\\\|x-8| \leq 2\\\\-2 \leq x-8 \leq 2\\\\6 \leq x \leq 10[/tex]
Is y=6x proportional?
Answers
y = 6x is proportional.
Proportionality between x and y is defined if there is a constant of proportionality 'k' such that y = kx.
So here, the constant of proportionality in y = 6x is 6.
This equation also means that y varies directly with respect to x and then 6 is the constant of variation.
That is, y is directly proportional to x.
Then a change in y implies a corresponding change in x in the same direction as that of y.
If x increases, then y also increases and if x decreases, then y also decreases.
These changes are related to the constant of proportionality 6.
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Find the value of x and XZ if Y is between X and Z, XY = 19, YZ = 2x+5,
and XZ = 6x + 12.
Answers
The values of x and XZ, calculated by the given equations are 3 and 30 respectively.
What is a equation?
The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.
Given information (and equations) in the question:
Y is between X and Z,
XY = 19,
YZ = 2x+5,
XZ = 6x+12
Since the question say Y is between X and Z, it means:
XY + YZ = XZ
Substituting the values in this equation by the values given in the question:
19 + 2x + 5 = 6x + 12
24 - 12 = 4x
x = 3
putting the value of x in the given equation:
XZ = 6x + 12
XZ = 6(3) + 12
XZ = 18 + 12
XZ = 30
Hence, the values of x and XZ are 3 and 30 respectively.
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choose if the following statement is true or false: correlation is sensitive to the scale of the data; however, covariance is not sensitive to the scale of the data
Answers
Correlation is not sensitive to the scale of the data; however, covariance is sensitive to the scale of the data, so the statement is false.
Covariance is a term used in statistic and regression analysis. Covariance shows how two variables differ.
Covariance is affected by the change in scale, for example if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by the same or another constant all together, then the covariance is automatically changed.
Correlation is also a term used in regression analysis and statistics. Correlation shows how two variables are related and therefore not influenced by the change in scale.
Hence the given statement is False
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given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
Answers
The value of g(x) is [tex]\frac{x^{2} }{3x-1}[/tex] of a function f(x)=3x-1 and (f∘g)(x)=[tex]x^{2}[/tex] .
As the composite equation is [tex]f(X)=3x^{}-1[/tex]
[tex](FOG)= x^{2}[/tex]
As [tex](FOG) =f(gx^{})\\[/tex]
∴ [tex]3x-1(gx)=x^{2}[/tex]
⇒ [tex]gx=\frac{x^{2} }{3x-1}[/tex]
How to solve the Equation of (fog)?(fog)(x) = f(g(x)) is pronounced "f of g of x" or "f constructed with g of x." Keep in mind that the letters in each expression for the composition remain in the same order.
A composite function is a fog. G(x) function is in f(x) function if (fog) is true. (Gof) indicates that f(x) function is in g(x) function.
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The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form. Ratio (red to blue) of the perimeters: Ratio (red to blue) of the areas: pleas help
Answers
Answer:
5/8 and 25/64
Evaluate the expression when x=5The expression is 4x -13.
Answers
To answer this question, we only need to replace x by 5, and then solve the resulting operations:
[tex]x=5\Rightarrow4x-13=4\cdot(5)-13=20-13=7[/tex]Therefore, the value for the expression 4x-13 when x = 5 is equal to 7.
acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. to ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.
Answers
Let X represent the number of defects.
When n=20 and p = 0.01,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.01)^0 * (1-0.01)^(20) + 20C1 * (0.01)^1 * (1-0.01)^(20-1) = 0.9831
When n=20 and p = 0.02,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.02)^0 * (1-0.02)^(20) + 20C1 * (0.02)^1 * (1-0.02)^(20-1) = 0.9401
When n=20 and p = 0.05,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.05)^0 * (1-0.05)^(20) + 20C1 * (0.05)^1 * (1-0.05)^(20-1) = 0.7358
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Nina bought 1.725 pounds of pecans and 1.83
pounds of almonds. She also bought twice as many
pounds of walnuts as pecans. How many more
pounds of walnuts did she buy than almonds?
Answers
Nina bought 3.45 pounds of walnut.
Nina bought 1.62 pounds more walnut than almonds
Quantity of pecan bought by Nina = 1.725 pounds
Quantity of almonds bought by Nina = 1.83 pounds
The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.
Quantity of walnuts = 2*Quanitity of pecans
= 2*1.725
= 3.45 pounds
So, she bought 3.45 pounds of walnut
Pounds of walnuts bought more than the almonds = Quantity of walnuts bought by Nina - Quantity of almonds bought by Nina
= 3.45 - 1.83
= 1.62 pounds
So, she bought 1.62 pounds more walnuts than almonds
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Ahouseis13feettall.Itsshadowis40feetlongatthesametimetheshadowofanearbybuildingis340feetlong.Findtheheightofthebuilding.
Answers
the red triangle is the building
the black triangle is the house
x is the height of the building
we have a problem of Tales triangles semblants so we can use this equalities
[tex]\begin{gathered} \frac{x}{340}=\frac{13}{40} \\ x=\frac{13(340)}{40}=110.5\text{ f}eet \end{gathered}[/tex]the height of the building is 110.5 feet
if luna adds 1/2 cups of flour to a mixing bowl for a recipe 5 times, how much flour has she added?
Answers
Answer:
10 cups
I hope this helps, have a great day/night!
At noon the temperature was 45°F. At
7 A.M. the temperature was 17°E.colder.
The temperature at 7 P.M. Was 4°F .
warmer than at 7 A.M. What was the.
temperature at 7 P.M.?
Answers
The temperature at 7 P.M is 32 °F.
What is a temperature in fahrenheit?Fahrenheit temperature scale, scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
Given that,
Temperature at noon = 45 °F
At 7 A.M. the temperature was 17°F colder = 45-17
= 28 °F
The temperature at 7 P.M. Was 4°F warmer than at 7 A.M
= At 7 A.M. the temperature was 17°F colder + 4°F
= 28+4
= 32 4°F
Hence, The temperature at 7 P.M is 32 °F.
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12.8 = 4v solve for v
Answers
Answer:
v=3.2
Step-by-step explanation:
12.8 = 4v
v= 12.8/4 isolate the variable and divide.
v= 3.2 Answer
Use your equation to complete the table. grams of fish 1500 number of calories 3000
Answers
Answer:
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
5+5=10
Which list shows the values in order from least to greatest?
0-0.5
√(0.5)
0-0.5
20% √/0.5
○ 20% |−0.5| √/0.5
○ = √/0.5 |−0.5| 20%
20%
Answers
The values in order from least to greatest are 0-0.5,√(0.5),20%,20% √/0.5,√/0.5 |−0.5| 20%. we eliminate 0-0.5 because the value is two times in the option.
What is the percentage?Percentage represents a proportion or a fraction of a whole, expressed as a portion of 100. It is commonly denoted by the symbol "%" (percent), which literally means "per hundred."
According to the given information:
The values in the list are:
0-0.5 = a range of values from 0 to 0.5, inclusive
√(0.5) ≈ 0.7071
20% = 0.2
20% √/0.5 = 0.2 * √(0.5) ≈ 0.1414
√/0.5 |−0.5| 20% = √(0.5) * |−0.5| * 0.2 ≈ 0.0707
Therefore, the correct list in order from least to greatest is:
0-0.5
√(0.5)
20%
20% √/0.5
√/0.5 |−0.5| 20%
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5 men take 28 days to build a boat. Assuming the men work at the same rate, calculate the number of men needed to build a boat in 20 days.
Answers
? men - 20 days
Cross multiplication:
(20x5)/28=3.57…≈4
An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin
Answers
An expression that could represent the price of the item after the discount is 0.8y.
Given that, an item costs y dollars and then a 20% discount is applied.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Cost price = $y and Discount percentage = 20%
Discount = 20% of y
= 20/100 × y
= 0.2y
The price of the item after the discount = y-0.2y
= 0.8y
Therefore, an expression that could represent the price of the item after the discount is 0.8y.
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