Answer:
a) 0.5447
b) 0.0228
c) 0.4325
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.
This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 9.6}{2.3}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a p-value of 0.5675
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 9.6}{2.3}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.
1 - 0.5675 = 0.4325
0.4325 probability that a randomly received emergency call is of more than 10 minutes.
Choose the system for the graph.
========================================================
Explanation:
The darkest shaded region is in the northern most region. This region is above both blue boundary lines.
A sample point from this region is (5,2)
We'll plug these coordinates into the first inequality of choice A
[tex]3x+4y \le 12\\\\3(5)+4(2) \le 12\\\\23 \le 12\\\\[/tex]
which is false. So we can rule out choice A.
We can rule out choice B for the exact same reason.
The answer is between C and D
---------------------------
Let's plug those x,y coordinates into the first inequality of choice C
[tex]3x+4y \ge 12\\\\3(5)+4(2) \ge 12\\\\23 \ge 12\\\\[/tex]
which is true. So far, so good.
Now repeat for the second inequality of choice C
[tex]2x-5y \ge 10\\\\2(5)-5(2) \ge 10\\\\0 \ge 10\\\\[/tex]
which is false. We rule out choice C. Choice D is the only thing left, so it must be the answer.
---------------------------
Let's check the second inequality of choice D just for the sake of completeness
[tex]2x-5y \le 10\\\\2(5)-5(2) \le 10\\\\0 \le 10\\\\[/tex]
which is true.
We can see that (x,y) = (5,2) makes both inequalities of choice D to be true, and therefore we have found the final answer.
Answer: TRUST ITS THE CHOICE D
Step-by-step explanation:
A business is interested in employees’ job satisfaction. The regional manager places a name card for every employee into a bowl and randomly selects 10 cards. Which sampling method was used?
cluster sampling
simple random sampling
stratified random sampling
systematic random sampling
Answer:
B
Step-by-step explanation:
Answer: simple random sampling
AKA: B
Step-by-step explanation: guy above me is correct :)
The formula for the surface area of a cylinder is:
SA = 2π r 2 + 2πrh note: that π= 3.14
a. Solve for h showing all work.
b. If the height of a can of soup is 5 inches and the radius is 1.5 inches, what is the surface area?
Answer:
Below in bold.
Step-by-step explanation:
a. SA = 2π r^2 + 2πrh
2πrh = SA - 2π r^2
h = (SA - 2πr^2)/2πr
When π = 3.14 we have
h = (SA - 6.28r^2)/ 6.28r
b. SA = 6.28*1.5^2 + 6.28*1.5* 5
= 61.23 in^2
An elevation of - 12 m is higher than an elevation of -17 m. An elevation of - 17 mis lower than an elevation of -14 m. Which set of inequalities correctly
expresses these relationships?
-12-17 and -17<-14
-12-17 and -17 > -14
-12<-17 and -17 < -14
-12-17 and -17 > -14
help plss
Given:
An elevation of - 12 m is higher than an elevation of -17 m.
An elevation of - 17 m is lower than an elevation of -14 m.
To find:
The set of inequalities that correctly expresses these relationships.
Solution:
An elevation of - 12 m is higher than an elevation of -17 m.
We know that, higher than means greater than and it is represented by the inequality ">". So,
[tex]-12>-17[/tex]
An elevation of - 17 m is lower than an elevation of -14 m.
We know that, lower than means less than and it is represented by the inequality "<". So,
[tex]-17<-14[/tex]
Therefore, the required set of inequalities is [tex]-12>-17[/tex] and [tex]-17<-14[/tex].
Note: The inequality signs are not proper in the options.
Let r be the binomial random variable corresponding to the number of people that will live beyond their 90th birthday,
r ≥ 15.
We want to find
P(r ≥ 15)
using the normal approximation given 625 trials and a probability of a 4.4% success on a single trial.
Answer:
P(r ≥ 15) = 0.9943.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
625 trials and a probability of a 4.4% success on a single trial.
This means that [tex]n = 625, p = 0.044[/tex]
Mean and standard deviation:
[tex]mu = E(X) = np = 625*0.044 = 27.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{625*0.044*0.956} = 5.13[/tex]
P(r ≥ 15)
Using continuity correction, this is [tex]P(r \geq 15 - 0.5) = P(r \geq 14.5)[/tex], which is 1 subtracted by the p-value of Z when X = 14.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14.5 - 27.5}{5.13}[/tex]
[tex]Z = -2.53[/tex]
[tex]Z = -2.53[/tex] has a p-value of 0.0057
1 - 0.0057 = 0.9943
So
P(r ≥ 15) = 0.9943.
Use the frequency distribution to construct a histogram. Using a loose interpretation of the requirements for a normal distribution, does the histogram appear to depict data that have a normal distribution? Why or why not?
Answer: hello the complete question is attached below
answer:
Histogram B is the right histogram
Yes it approximately depict data that have a normal distribution
Step-by-step explanation:
The histogram when plotted is symmetric which means/depicts that the data provided have a normal distribution ( approximately )
A histogram is one of the graphical ways of representing data for easy reading and interpretation.
Please help ASAP ASAP
Step-by-step explanation:
[tex] \sqrt{53} [/tex]
No step by steps or links please
Answer:
Six at top, ten at second, twenty-seven at third, and four at bottom.
PLEASE HELP ME ASAP! ILL GIVE YOU ALL OF MY POINTS PLEASE HELP.
A large container of breath mints has a mass of 50 g. A small container has a mass of 10 g. What is the percent decrease from the mass of the large container to the mass of the small container? Show your work.
Answer:
80 percent decrease
Step-by-step explanation:
80% of 50 = 40 and 50 - 40 = 10
Answer:
It decreases 80%
Step-by-step explanation:
If the 50g one is 100%, and the 10g one is a fraction of that, find out what 10/50 is as a percent.
10/50= 20%
Because this is the remaining mass, the other 80% has been deducted meaning that the mass of the large container has decreased 80% to get to the mass of the smaller one.
cos(x+pi/3)-sin2x=0 ahihihihihihiihihihihihih
Answer:cos(x+pi/3) - sin2x=0
<=> cos(x+pi/3)=sin2x
<=> cos(x+pi/3)=cos(pi/2-2x)
<=>x+pi/3=pi/2-2x+k2pi
Or x+pi/3=-pi/2 +2x+k2pi
<=>x=pi/18 + k2pi/3
Or x=5pi/6 +k2pi
Step-by-step explanation:
if (x) - **4, g(x) = x= 2, and h(x) = 4x+1, what is (f• Hºg)(x)?
2x+16
o (fe hºg)(x) =
2x+4
o (fonog)(x)=
4x-3
o (f• hºg)(x)- Ax=1
4x-5
o (f• nºg)(x) = AX-
Answer:
c
Step-by-step explanation:
A pizza company runs a marketing campaign based on their delivery time for pizzas. They claim that they will deliver a pizza within 30 minutes of ordering or it is free. In practice the time it takes to prepare a pizza and it being delivered is normally distributed with mean 25 minutes and standard deviation 3 minutes. What is the probability a pizza is delivered for free?On a particular Sunday, 40 pizzas were ordered. What is the probability that more than 2 were delivered for free?If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
Answer:
0.0475 = 4.75% probability a pizza is delivered for free.
0.2955 = 29.55% probability that more than 2 were delivered for free.
The delivery time should be advertised as 32 minutes.
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the normal distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25 minutes and standard deviation 3 minutes.
This means that [tex]\mu = 25, \sigma = 3[/tex]
What is the probability a pizza is delivered for free?
More than 30 minutes, which is 1 subtracted by the p-value of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 25}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525
1 - 0.9525 = 0.0475
0.0475 = 4.75% probability a pizza is delivered for free
What is the probability that more than 2 were delivered for free?
Multiple pizzas, so the binomial probability distribution is used.
0.0475 probability a pizza is delivered for free, which means that [tex]p = 0.0475[/tex]
40 pizzas, which means that [tex]n = 40[/tex]
This probability is:
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{40,0}.(0.0475)^{0}.(0.9525)^{40} = 0.1428[/tex]
[tex]P(X = 1) = C_{40,1}.(0.0475)^{1}.(0.9525)^{39} = 0.2848[/tex]
[tex]P(X = 2) = C_{40,2}.(0.0475)^{2}.(0.9525)^{38} = 0.2769[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1428 + 0.2848 + 0.2769 = 0.7045[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.7045 = 0.2955[/tex]
0.2955 = 29.55% probability that more than 2 were delivered for free.
If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
The 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 25}{3}[/tex]
[tex]X - 25 = 2.327*3[/tex]
[tex]X = 32[/tex]
The delivery time should be advertised as 32 minutes.
In a bag of mini candy bars, 40% of the candy bars are Snickers. There are 120 Snickers in the bag. How many total mini candy bars are in the bag?
Answer:
The amswer is 48.
Step-by-step explanation:
120×0.40=48
In communicating with an orbiting satellite, suppose that a 30-bit message is sent to thesatellite. Transmission of messages can sometimes be distorted. If the probability of eachbit being received incorrectly is 0.001, where each bit is received independently of the others,what is the probability that at least one bit is received incorrectly?
Answer:
0.0296 = 2.96% probability that at least one bit is received incorrectly.
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is received correctly, or it its not. Each bit is received independently of the others, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of each bit being received incorrectly is 0.001
This means that [tex]p = 0.001[/tex]
30-bit message
This means that [tex]n = 30[/tex]
What is the probability that at least one bit is received incorrectly?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.001)^{0}.(0.999)^{30} = 0.9704[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9704 = 0.0296[/tex]
0.0296 = 2.96% probability that at least one bit is received incorrectly.
What is cos 0 when sin 0= 2/3
Answer:
your answer is √7/3
Step-by-step explanation:
your answer is √7/3
If a product normal retails for $40, and a customer has a coupon for 15% off, what will the discounted price of the product be?
Answer:
$34
Step-by-step explanation:
price of the product = $40
coupon = 15% off
discount price = 15% of price of a product
=15/100 * $40
=$600/100
=$6
New price of the product = original price - discount
=$40 - $6
=$34
Which of the following represents the difference between ten and a number is the sum of eight and a number"?
10 - N(8 + N)
08-N = 10 +N
10 -N = 8+N
9514 1404 393
Answer:
(c) 10 -N = 8 +N
Step-by-step explanation:
The difference between 10 and a number is (10 -N).
The sum of 8 and a number is (8 +N).
In this context, "is" means "equals," so we have ...
10 -N = 8 +N
Which type of parent function is f(x) =1/2
Answer:
I think you are missing something unless the answer is a horizontal line.
Step-by-step explanation:
Answer:
square root
Step-by-step explanation:
just took the test :)
Give an
example of a set of data that has more than one mode.
Answer:
Step-by-step explanation:
To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.
A data set can have more than one mode if there is more than one value with the highest count. For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.
Example of a set of data having more than one node is {1; 2; 2; 3; 3}.
What is Node?
An example S of the data type node. set is a subset of the nodes of a graph G. S is said to be valid for the nodes of G.
Given,
To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.
Now,
A data set can have more than one mode if there is more than one value with the highest count.
For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.
Learn more about node,
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My sister’s house is 1 2/4 times as high as my house. My house is 5 feet high. How high is my sister’s house?
Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit
together?
Answer:
The total number of ways A, B, C, D, and E can sit together is 5
Step-by-step explanation:
Consider the following system of equations:
y = −2x + 3
y = x − 5
Which description best describes the solution to the system of equations?
Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.
Line y = −2x + 3 intersects line y = x − 5.
Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.
Line y = −2x + 3 intersects the origin.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Line y = −2x + 3 intersects line y = x − 5."
»»————- ★ ————-««
Here’s why:
When the system of equations are graphed, they would intersect at a point. This means that there is a solution to the system. The solution is [tex](\frac{8}{3} ,-\frac{7}{3} )[/tex].While the statement that the lines intersect the x-axis is true, the question asks the statement that describes the solution. The solution is the point of intersection between the two lines.⸻⸻⸻⸻
See the Graph Attached
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than and draw a sketch of the region.
Answer:
0.5000
Step-by-step explanation:
According To The Question,
The Area under the Standard Normal Curve, We Can Use the Statistical Tables , That Reported Area As P(z < a) .
Thus, We need to use the following Relationship.
P(z > a) = 1 - P(z < a)Now solve, P(z > 0) = 1 - P(z < 0) ⇔ 1 - 0.5000 ⇔ 0.5000
(Diagram, Please Find in Attachment)
Express square root 4x – 7 as a power .
Answer:
It's answer is 4x-7^1/2
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
\text{7 is added to a number.}
7 is added to a number.
Answer:
7+x
Step-by-step explanation:
X will be the unknown
By how much is the sum of 3 2/3 and 2 1/5 less than 7
Step-by-step explanation:
32/3+21/5÷7
14.87÷7
2.124
How many liters each of a 25% acid solution and a 50% acid solution must be used to produce 80 liters of a 40% acid solution?
Answer:
32 and 48 litersStep-by-step explanation:
Let 25% solution is x liters, then 50% solution is (80 - x) liters.
Acid content is going to be same:
0.25x + 0.5(80 - x) = 80*0.40.25x - 0.5x + 40 = 320.25x = 8x = 8/0.25x = 32 litersSo 32 liters of 25% solution and 80 - 32 = 48 liters of 50% solution
Is 4 over 5 equals 48 over 60 a true proportion?
Answer:
0.8 you yes both of them has the same answer , so it is a true portion
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{48}{60}[/tex]
This is a true proportion because when you cross multiply you get the same product.
[tex]48*5=240[/tex]
[tex]4*60=240[/tex]
11 Roger has m toy cars. Don has twice as many cars as Roger. Larry has five more cars than Roger. Write down an expression, in terms of m, to complete each statement. Don has cars H Larry has cars
Step-by-step explanation:
Roger has m toy cars.→ Number of cars Roger has = m
Don has twice as many cars as Roger.→ Number of cars Don has = 2(Cars Roger has)
→ Number of cars Don has = 2m
Larry has five more cars than Roger.→ Number of cars Larry has = 5 + (Cars Roger has)
→ Number of cars Larry has = 5 + m
what is the average rate of change from 0 to 2 of the function represented by the graph? Enter your answer, as a simplified fraction, in the box
Answer:
=>The graph of an exponential relation is also non-linear.
=>The graph of an exponential relation becomes nearly parallel to x-axis on one and then curves upward and becomes nearly parallel to the y-axis on the other sid.
The average rate of change from 0 to 2 of the function represented by the graph is [tex]\frac{3}{2}[/tex].
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
According to the question
[tex]x_{1} =0[/tex], [tex]x_{2} =2[/tex]
f(0) = 1, f(2) = 4
The average rate of change = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]
= [tex]\frac{f(2)-f(0) }{2-0 }[/tex]
= [tex]\frac{4-1}{2}[/tex]
= [tex]\frac{3}{2}[/tex]
Hence, the average rate of change from 0 to 2 of the function represented by the graph is [tex]\frac{3}{2}[/tex].
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