The random variable X is normally distributed with mean x = 174 and standard deviation o = 20. Find the probability of (a) P(X > 170) (1) P(X < 182) (e) P(160 < X < 170) (d) P(172 < X <192).
Answers
(a) The probability of P(X > 170) can be found using the standard normal distribution. Similarly, probabilities for P(X < 182), P(160 < X < 170), and P(172 < X < 192) can also be calculated using the standard normal distribution after standardizing the values based on the given mean and standard deviation.
To find the probabilities using the standard normal distribution:
(a) P(X > 170):
1. Standardize the value of 170 using the given mean and standard deviation: z = (170 - 174) / 20 = -0.2.
2. Look up the corresponding z-value in the standard normal distribution table or use a calculator to find the area to the left of -0.2.
3. Subtract the area obtained in step 2 from 1 to find the probability: P(X > 170) = 1 - P(Z < -0.2).
(b) P(X < 182):
1. Standardize the value of 182: z = (182 - 174) / 20 = 0.4.
2. Look up the corresponding z-value to find the area to the left of 0.4 in the standard normal distribution.
3. This area represents the probability P(X < 182).
(c) P(160 < X < 170):
1. Standardize both values of 160 and 170 separately: z1 = (160 - 174) / 20 and z2 = (170 - 174) / 20.
2. Look up the corresponding z-values in the standard normal distribution to find the areas to the left of z1 and z2.
3. Subtract the area obtained in step 2 for z1 from the area obtained for z2 to find the probability P(160 < X < 170).
(d) P(172 < X < 192):
1. Standardize both values of 172 and 192 separately: z1 = (172 - 174) / 20 and z2 = (192 - 174) / 20.
2. Look up the corresponding z-values in the standard normal distribution to find the areas to the left of z1 and z2.
3. Subtract the area obtained in step 2 for z1 from the area obtained for z2 to find the probability P(172 < X < 192).
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Related Questions
what kinds of images are based on mathematical instructions that define lines, curves, text, ovals, and other geometric shapes?
Answers
The mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
The vector graphics is defined as the computer graphics that the visual images are created directly from geometric shapes. It is defined on the Cartesian plane such as lines, curves, texts, ovals and other geometric shapes
The vector artworks are the artwork that created by vector graphics. There will be lines curves, text, oval and other geometric shapes according to the mathematical expression
Therefore, the vector graphics is the mathematical instruction that defines the geometric shapes
Hence, the mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
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If angle ABC is complementary to angle BCA and angle ABC=4x while angle BCA=11x, first find x and then find the measures of each angle.
Answers
Answer:
x = 6
ABC = 24
BCA = 66
Step-by-step explanation:
Complementary angles equal 90°
4x + 11x = 90
Add 4x and 11x
15x = 90
Divide by 15
x = 6
Replace x with 6
4 · 6 = 24
11 · 6 = 66
Check:
24 + 66 = 90
I hope this helps!!!
how many 15 kilocalories to calories?
Answers
15 Kilocalorie (international) (kcal) = 15000 Calorie (cal)
Kilocalorie (international) :The kilocalorie, sometimes call kilogram calorie is a measurement unit of energy. It is defined as the amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius. The symbol of kilocalorie is kcal. The kilocalorie is commonly used in measuring the calorific, heating, or metabolizing value of foods. It is equal to 1000 calories, or approximately 4.2 kilojoules.
Calorie :The calorie is a pre-SI metric unit of energy. Its symbol is cal, and first defined as a unit of heat by Nicolas Clément in 1824. The calorie is commonly used in the field of chemistry, and in many countries it is commonly used as a unit of food energy. There are two defined for the calorie, gram calorie (approximately equals 4.2 joules) and kilogram calorie (approximately equals 4.2 kilojoules).
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Raymond is four times as old as christine plus 5 years.Write an algebraic expression for Raymonds age in terms of christine age
Answers
Answer:
4c + 5 = R
Step-by-step explanation:
This should help you
What are the MRSs? Determine if there is a diminishing MRS
a. U(x,y)=3x+y
b. U(x,y)=x.y
c. U(x,y)=x⋅y
d. U(x,y)=x2−y2
e. U(x,y)=x+yx.y 3.
Consider each of a. U(x,y)=x0.1y0.4 b. U(x,y)=min(αx,βy) c. U(x,y)=αx+βy calculate the following i. Demand curves for x and y ii. Indirect utility function iii. (Indirect) expenditure function iv. Show that the demand curve is homogeneous in degree zero in terms of income and prices
Answers
a. The MRS is constant (not diminishing) at 1/3.
U(x,y) = 3x + y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / 3
The MRS is constant (not diminishing) at 1/3.
b. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
The MRS is diminishing because as y increases, the MRS decreases.
c. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.
d. The MRS depends on the ratio of y to x and can vary.
U(x,y) = x^2 - y^2
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x
The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.
e. The MRS depends on the values of x and y and can vary.
U(x,y) = x + y / (x * y)
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)
The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.
Now let's move on to the second part of the question:
For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.
To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.
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in abc, angle a = 90 and an is the altitude. if ab = 20 and AC = 15, find BC, BN, NC, AN
Answers
The missing values are:
BC = 25, BN = 16, NC = 9, and AN = 12
Given:
AB = 20
AC = 15
Using the Pythagorean theorem in triangle ABC:
CB = √AC² + AB²
CB= √20² + 15²
CB= √625
CB= 25
Since, AN is altitude we have ΔNBA~ΔABC and ΔNAC~ΔABC
BN / AN = BA / CB
BN/ 20= 20/25
BN = 16
and, AN / BA = AC / CB
AN /20 = 15/ 25
AN = 12
Now, CN= CB - BN
CN = 25- 16
CN= 9
BC^2 = 20^2 + 15^2
BC^2 = 400 + 225
Since ΔANC is a right triangle so
AN = √15²-12²
AN = √81
AN = 9
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What are the next four multiples of 1/7
Answers
What are the next four multiples of 1/7 ?
so, it will be :
\(\begin{gathered} 2\cdot\frac{1}{7}=\frac{2}{7} \\ \\ 3\cdot\frac{1}{7}=\frac{3}{7} \\ \\ 4\cdot\frac{1}{7}=\frac{4}{7} \\ \\ 5\cdot\frac{1}{7}=\frac{5}{7} \end{gathered}\)12. A human resources director for a large corporation claims the probability a randomly
selected employee arrives to work on time is 0.95.
(a) If we take a random sample of 3 employees, what's the probability that all of them arrive on
time?
(b) If we take a random sample of 3 employees, what's the probability that none of them arrive
on time?
(c) If we take a random sample of 3 employees, what's the probability that at least one of them
arrives on time?
I
Answers
Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.857375 = 85.7375%.
b) 0.000125 = 0.0125%.
c) 0.999875 = 99.9875%.
What is the binomial distribution formula?The formula is:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
n = 3, p = 0.95.
Item a:
The probability is P(X = 3), hence:
P(X = 3) = (0.95)^3 = 0.857375 = 85.7375%.
Item b:
The probability is P(X = 0), hence:
P(X = 0) = (0.05)^3 = 0.000125 = 0.0125%.
Item c:
The probability is P(X > 0), hence:
P(X > 0) = 1 - P(X = 0) = 1 - 0.000125 = 0.999875 = 99.9875%.
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The ____ states that the sum of the measures of the interior angles of a triangle is 180°.
Koo
Answers
Write two expressions (with at least two terms each) that when added together have a sum of -4n + 6
Answers
Answer:
Identify the sequence, hten use the formula to find the first term a1=2
Identify the sequence, then use if the formula to find the second term a3=-6
Step-by-step explanation:
The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)
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 expression is;
- 4n + 6
Now the expression as
A. (-6n) + (6 + 2n)
After adding, we have;
(-6n) + (6 + 2n) = -6n + 6 + 2n
= - 4n + 6
B. (- 10n + 2) + (6n + 4)
After adding we have;
(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4
= - 4n + 6
Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)
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HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Answers
Given:
The function is:
\(f(x)=-4(1.09)^x\)
The table of values for the function g(x).
To find:
The equation that best compares the y-intercepts of f(x) and g(x).
Solution:
We have,
\(f(x)=-4(1.09)^x\)
Putting \(x=0\), we get
\(f(x)=-4(1.09)^0\)
\(f(x)=-4(1)\)
\(f(x)=-4\)
So, the y-intercept of the function f(x) is -4.
From the given table of values, it is clear that the function f(x) passes through the point (0,-4). So, the y-intercept of the function g(x) is -4.
The y-intercept of f(x) is equal to the y-intercept of g(x).
Therefore, the correct option is A.
Answer:
A) The y-intercept of f(x) is equal to the y-intercept of g(x).
An explanation on juypter notebook would be
great!!
Create an additional Series called next_month with the return of the market over the following 21 days: \[ \text { Next Month } h_{t}=\frac{P_{t+21}-P_{t}}{P_{t}} \]
Answers
One-liner code to create the "next_month" Series in Jupyter Notebook: ```python
next_month = (P.shift(-21) - P) / P
```
Jupyter Notebook is an open-source web application that allows you to create and share documents containing live code, visualizations, and explanatory text. It supports various programming languages, but it is commonly used with Python for data analysis, scientific computing, and machine learning tasks.
Jupyter Notebook provides an interactive environment where you can execute code cells and see the results immediately, which makes it a popular choice among data scientists and researchers.
To get started with Jupyter Notebook, you need to install it on your local machine or use an online service that provides Jupyter Notebook functionality. Once you have it set up, you can create a new notebook or open an existing one.
Now, let's move on to creating the `next_month` Series based on the formula you provided. I assume you have a time series of stock market prices stored in a pandas Series called `market_prices`. To calculate the return over the following 21 days, we can use the formula:
\(\[ \text {Next Month } h_{t}=\frac{P_{t+21}-P_{t}}{P_{t}} \]\)
Here's an example code snippet that demonstrates how you can calculate the `next_month` Series using pandas in a Jupyter Notebook:
```python
import pandas as pd
# Assuming you have a Series of market prices
market_prices = pd.Series([100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210])
# Calculate the return over the following 21 days
next_month = (market_prices.shift(-21) - market_prices) / market_prices
# Display the result
print(next_month)
```
In the code snippet above, we import the pandas library and create a Series called `market_prices` with sample data. The `shift()` function is used to shift the Series forward by 21 days, and then we subtract the original `market_prices` from the shifted Series.
Finally, we divide the difference by the original `market_prices` to get the return as a fraction. The result is stored in the `next_month` Series.
You can execute this code cell in Jupyter Notebook by selecting it and pressing the "Run" button or using the keyboard shortcut (usually Shift + Enter). The output will be displayed below the code cell, showing the values of the `next_month` Series based on the provided formula.
That's it! You now have the `next_month` Series containing the return of the market over the following 21 days. Feel free to modify the code or adapt it to your specific needs.
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HELP ASAPPP!! If M(1,7) is the midpoint of the line segment AB and if A has coordinates (-4,-4) find the coordinates of B.
Answers
Answer:
(-15,7)
Step-by-step explanation:
I did it on desmos
what is 10 times 643 rounded to the nearest hundered
Answers
Answer:
6400
Step-by-step explanation:
643 × 10 = 6430
Nearest hundredth is the third last digit so it should be the number 4
Since the digit after 4 is less than 5, we keep the number the same
The answer you should get is 6400
sheet of paper.
Allison bought a tennis racket for $25, 2 cans of tennis balls for $5 each
can, a tennis shirt for $15.50, and a pair of tennis shoes for $75. How
much change did she freceive from $140?
Answers
Answer:
14.5$ from the money
addsing the expense
Answer:
total rupees 120.5. Please Mark it as brainlist answer.
In a picture, there are 40 monkeys, and 60% of the monkeys are in the trees.
How many monkeys are in the trees? Use a 10-squares model to explain your answer.
please answer. ANSWER the question CORRECTLY. please explain your answer with 10 square model. I dislike useless answers. i dont want only the answer, also the explanation. please.
Answers
Answer:
The number of monkeys in the trees is 24
Step-by-step explanation:
Label each of the lines from 10 - 40 and then fill the box in from there.
Also explanation: 0.6 x 40 = 24
Beau currently has saved $ 10000 in a CD paying 5% each year. How much compound interest will Beau have earned after 73 years? Round to the nearest cent.
Answers
Beau will have earned approximately $169,645.12 in compound interest after 73 years.
To calculate the compound interest, we use the formula:A = P(1 + r/n)^(nt)
Where:
A is the final amount,
P is the initial principal (amount saved),
r is the annual interest rate (expressed as a decimal),
n is the number of times interest is compounded per year,
and t is the number of years.
In this case, Beau has saved $10,000, the interest rate is 5% (or 0.05 as a decimal), and the interest is compounded annually (n = 1). Beau is saving for 73 years (t = 73).
Plugging these values into the formula, we have:A = 10000(1 + 0.05/1)(1*73)
Calculating the exponent and rounding to the nearest cent, we find that Beau will have earned approximately $169,645.12 in compound interest after 73 years.
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Solve for x
triangle abc is similar to triangle aed
Answers
Answer:
9/5 or 1.8
Step-by-step explanation:
triangle aed is larger than triangle abc by a scale factor of 5; we know this because side ed is 5 units and cb, the corresponding side in triangle abc, is 1. if ad has a length of 9, the length of ab must be 9 divided by five. thus, z is equal to 9/5 or 1.8.
SALE
25% OFF
original price!
During the sale, Ronald paid $77 for a hammock.
What was the original price rounded to the nearest penny?
A $102.67
B) $204.88
C$104.28
D$156.83
Answers
Determine the center and radius of the following circle equation:
+ y2 – 123 + 8y – 48 = 0
Answers
Do you want the steps on how to get it?
Answer:
it's 10
Step-by-step explanation:
don't know the steps
for 105 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. each day, she took a sample of 9 bottles. the average across all 945 bottles (105 days, 9 bottles per day) was 52 degrees fahrenheit. the standard deviation across all bottles was .9 degrees fahrenheit. when constructing an x-bar chart, what would be the upper control limit?
Answers
The upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit for standard deviation.
To find the upper control limit for an x-bar chart, we use the formula:
Upper Control Limit = X-bar + A2 * (standard deviation / \(\sqrt{(sample size)}\))
Where X-bar is the average temperature across all bottles (52 degrees Fahrenheit), A2 is a constant factor based on the sample size (for a sample size of 9, A2 is 0.729), and the standard deviation is 0.9 degrees Fahrenheit.
Plugging in these values, we get:
Upper Control Limit = 52 + 0.729 * (0.9 / \(\sqrt{9}\))
Upper Control Limit = 52 + 0.243
Upper Control Limit = 52.243 degrees Fahrenheit
Therefore, the upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit. This means that if any sample of 9 bottles has an average temperature above this limit, it may indicate a problem with the process that needs to be addressed.
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The upper control limit (UCL) for the X-bar chart is 52.9 degrees Fahrenheit.
We will use the following terms to find the upper control limit (UCL) for an X-bar chart:
Average temperature (µ) = 52 degrees Fahrenheit
Standard deviation (σ) = 0.9 degrees Fahrenheit.
Sample size (n) = 9 bottles
Number of days (m) = 105 days.
To find the UCL, we first need to find the standard error (SE) using the formula:
SE = σ / √n
Substitute the given values into the formula:
SE = 0.9 / √9 = 0.9 / 3 = 0.3 degrees Fahrenheit
Now we'll use the control chart formula to find the UCL, which is:
UCL = µ + 3 * SE
Substitute the values:
UCL = 52 + 3 * 0.3 = 52 + 0.9 = 52.9 degrees Fahrenheit.
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Can I get help please
Answers
The amount of money that I will have at the end of 20 years would be =$4,480. That is option D
What is compound interest?Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.
The total amount invested (p)= $2,000
The rate of investment (r) = 5%
The time of investment(t)= 12 year
The compound interest warm from that account;
= P×T×R/100.
= 2,000×12×5/100
= 120000/100
= $1200
For the next 8 years with the rate of 8% ;
= 2,000×8×8/100
= 128000/100
= $1280
The total compound interest = $1200+$1280= $2,480
Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480
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Select the correct answer. what is the value of the third quartile of the data set represented by this box plot? a box plot with lower quartile, median and upper quartile values as 21, 26, and 29, respectively. the whiskers on both the ends end at 19 (minimum) and 33 (maximum). a. 19 b. 21 c. 26 d. 29
Answers
Answer:
D. 29
Step-by-step explanation:
just did the test and got it correct. Edmentum, Plato.
-70÷ (-1)
How do i get the solution??
Answers
Any expression divided by -1 equals its opposite, turning -70 into positive 70.
Answer:
70
Step-by-step explanation:
-70 / -1
= 70 / 1
= 70
Full explanation Please
Will mark brainlist
Answers
Answer:12.04
Step-by-step explanation:
A^2 +B^2=C^2- pythag formula
8x8=64
9x9=81
64+81 =145
c= root 145 square root it as a squared + b squared = c squared
c=12.0415
1 kilograms of pears cost as much as 1. 5 kilograms of apples. Alex paid $34. 20 for 4 kilograms of pears and 3 kilograms for apples. How much did 1 kilogram of pears cost?
Answers
The cost of 1 kilogram of pears is $5.70.
How determine the costThe cost of 1 kilogram of pears can be found by using the given information and setting up an equation. First, let's repeat the question: "1 kilogram of pears cost as much as 1.5 kilograms of apples. Alex paid $34.20 for 4 kilograms of pears and 3 kilograms for apples. How much did 1 kilogram of pears cost?"
Let's assign variables to the unknowns:
- P = cost of 1 kilogram of pears
- A = cost of 1 kilogram of apples
From the question, we know that:
- 1P = 1.5A - 4P + 3A = 34.20
Now, we can use substitution to solve for P.
1. Substitute 1.5A for P in the second equation: 4(1.5A) + 3A = 34.20
2. Simplify: 6A + 3A = 34.20
3. Combine like terms: 9A = 34.20
4. Solve for A: A = 34.20/9 A = 3.8
5. Substitute 3.8 for A in the first equation: 1P = 1.5(3.8)
6. Solve for P: P = 5.7
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Tom wants to buy his wife a bouquet of flowers for their anniversary. He decides to get them delivered to her work. Tom spends 20 dollars on the roses. He is charged $1.25 per rose and an additional $5 for a card. How many roses did Tom send his wife?.
Answers
Tom sent 16 roses to his wife
Step-by-step explanation:
20/1.25=16
first you have to get the cost of each rose then divide that by 20 to get the total amount of roses received
4# is a two digit number ,where # represents the digit at ones place . 7999 ÷ 4# lies between ---------
Answers
Answer:
\(7999 \div 4\#\) lies between 163.245 and 199.975
Step-by-step explanation:
Given
2 digit = 4#
Required
The range of \(7999 \div 4\#\)
Let
\(\# = 0\) --- the smallest possible value of #
So:
\(7999 \div 40 = 199.975\)
Let
\(\# = 9\) --- the largest possible value of #
So:
\(7999 \div 49 = 163.245\)
Hence, \(7999 \div 4\#\) lies between 163.245 and 199.975
Triangle JKL is similar to triangle TUV. Find the missing side length of triangle TUV.
A. 10.6
B. 6
C. 6.2
D. 5.8
Answers
Answer:
B) 6 inches
Step-by-step explanation:
==>Given that ∆JKL ~ ∆TUV, it therefore means the ratio of proportion of the corresponding sides of ∆JKL and ∆TUV are equal.
Thus:
JK/TU = JL/TV = KL/UV
10/7.5 = 8/x = 13/9.75
Let's find x
10/7.5 = 8/x
=>Cross multiply
10*x = 8*7.5
10x = 60
Divide both sides by 10
x = 6 inches
Our answer is B) 6 inches
consider the correlation between heights of fathers and mothers and the heights of their sons. refer to the accompanying technology output. should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? why or why not?
Answers
Yes, the multiple regression equation should be used for predicting the height of a son based on the height of his father and mother because the P-value in the ANOVA table is very low.
What is multiple regression equation?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A single dependent variable and numerous independent variables can be analyzed using the statistical approach known as multiple regression. In order to forecast the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
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