Answer:
0.3632 = 36.32% probability that the mean benefit for a random sample of 20 patients is more than $4100.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Population: [tex]\mu = 4064, \sigma = 460[/tex]
Sample of 20: [tex]n = 20, s = \frac{460}{\sqrt{20}} = 102.86[/tex]
Find the probability that the mean benefit for a random sample of 20 patients is more than $4100.
This is 1 subtracted by the pvalue of Z when X = 4100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4100 - 4064}{102.86}[/tex]
[tex]Z = 0.35[/tex]
[tex]Z = 0.35[/tex] has a pvalue of 0.6368
1 - 0.6368 = 0.3632
0.3632 = 36.32% probability that the mean benefit for a random sample of 20 patients is more than $4100.
What is the place value of the digit 4 in the number 93493
Answer:
It is in the hundreds place
Step-by-step explanation:
If you could give brainliest it would be much appreciated.
Answer:
Step-by-step explanation:
Hundreds
Katy organised a wedding. Guests had to choose their meal from pasta , chicken or beef . 1/3 of the guests chose pasta . 5/12 of the guests chose chicken . 24 of the guests chose beef. How many guests were at the wedding ?
please help i’ll give brainliest
Answer:
There were 96 guests at the wedding.
Step-by-step explanation:
Let,
x be the total number of guests at the wedding.
People who chose pasta = 1/3 of the guests = [tex]\frac{1}{3}x[/tex]
People who chose chicken = [tex]\frac{5}{12}x[/tex]
People who chose beef = 24
Now,
[tex]\frac{1}{3}x+\frac{5}{12}x+24=x\\\\\frac{4x+5x+288}{12}=x\\9x+288 = 12x\\288=12x-9x\\288=3x\\3x=288[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{288}{3}\\x=96[/tex]
Hence,
There were 96 guests at the wedding.
Ashley’s school took a field trip. A total of 32 vehicles were needed for the trip. Some students took the bus, and some students car-pooled. There were 27 people on each bus and 3 people in each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?
Answer:
19 cars
13 buses
Step-by-step explanation:
We have a system of equations as follows
X + y = 32 -----1
3x + 27y = 408 ----2
x = car
y = bus
From equation 1
x + y = 32
x = 32 - y ---- 3
We put equation 3 into equation 2
3(32-y) + 27y = 408
96y -3y + 27y = 408
96 + 24y = 408
24y = 408 - 96
24y = 312
Divide through by 24 to get the value of y
Y = 312/24
Y = 13
We put the value of y in equation 3
x = 32 - 13
x = 19
So 19 cars would be needed for the trip and also 13 buses would also be needed
There are 1400 students in a school. 52% of them are female. How many are male?
Answer: out of 1400 students 672 of them are males.
Step-by-step explanation:
Step 1 turn the percent into a decimal
0.52*1400= 728
728 is the number of female students
Step 2 subtract 728 from 1400
1400-728=672
Hope this helps ;)
Eloise ran 2 3/12 miles yesterday and 1 8/12 miles today how far does Eloise run in all
Answer:
3 11/12
Step-by-step explanation:
Answer:
Different ways to answer
Step-by-step explanation:
mixed number: 3 11/12
decimal: 3.916 repeating
imporper fraction: 47/12
PLEASE MARK ME BRAINLIEST
Wake up to reality! Nothing ever goes as planned in this world. The longer you live, the more you realize that in this reality only pain, suffering and futility exist. ” – Uchiha Madara
I well know a social life its only pain heading your way i am just saying a dream girl that i wish that would exist i dont like when people try to tell me to get a social life and try to get friends when they turn on you and use you
I do go outside that does not mean i have to be social with other people i am not the same as them i never want to be friends with a person who only causes pain and suffering in life
Exactly, Thank you again for these quotes!
-p.s you are loved <3
EDIT: THANKS FOR THE POINTS >:3
A farmer raises only ducks and pigs. There are 55 animals in all on his farm, and 146 legs.
Find the number of ducks and pigs on his farm by setting up and solving a system of equations.
Define the variables
Equations
Show all work
Answer:
Number of ducks = 37
Number of pigs = 18
Step-by-step explanation:
Let,
x be the number of ducks
y be the number of pigs
According to given statement;
x+y=55 Eqn 1
2x+4y=146 Eqn 2 (As ducks will have 2 legs and pigs will have 4)
Multiplying Eqn 1 by 2
2(x+y=55)
2x+2y=110 Eqn 3
Subtracting Eqn 3 from Eqn 2
(2x+4y)-(2x+2y)=146-110
2x+4y-2x-2y=36
2y=36
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{36}{2}\\y=18[/tex]
Putting y=18 in Eqn 1
x+18=55
x = 55-18
x = 37
Hence,
Number of ducks = 37
Number of pigs = 18
At a university, 73% of the students are undergraduates. .
If there are 6,700 students, how many of them
are undergraduates?
Answer:4,891 are undergraduate students .
Step-by-step explanation:
Total Number of students = 6700
Percentage of Undergraduate students = 73%
Number of Undergraduatre students = Percentage of Undergraduate students x Total Number of students
= 73% x 6700
73/100 x6700
=4,891 are undergraduate students .
Pam is a wedding planner She is setting up a room to seat at least 100 guests. She has some tables that seat 10 people and some tables that seat 5 people. She only has 10 of the tables that seat 5.
1. Let x = the number of 10-person tables, and y = the number of 5-person tables. Write an inequality to describe the number of tables Pam could set up for the wedding.
2. Write a second inequality based on the fact that there are only 10 tables that seat 5.
Answer:
1. 10x + 5y ≥ 100
2. y ≤ 10
O will give te brainliest plz help
Answer:
B
Hope it helps uwu
is the graph of the function shown in the graph below one to one? why?
In accordance with functional theory, definition of functions and kinds of functions, the function is not injective but surjective. (Correct choice: C)
Does represent the picture of the function an injective or surjective function?
In accordance with functional theory, functions are relations in which each element of the domain is related to only one element of the range. There are three kinds of functions: (i) Injective - Each domain element is related to one distinct element of the range, (ii) Surjective - There are at least two domain elements that are related to an element of the range, (iii) Bijective - The function is both injective and surjective.
Based on all these information, we conclude that the given function has at least two values of the x-axis (domain) related to one value of the y-axis (range). In a nutshell, the function is not injective but surjective. (Correct choice: C)
To learn more on injective functions: https://brainly.com/question/1548798
#SPJ1
a² + 8a +15
Math problem hard
Answer:
Step-by-step explanation:
I believe u have to factorise
(a+3)(a+5)
I need help with this question, in the picture.
Answer:
34 degrees
Step-by-step explanation:
34 degrees
the angle is 90 degrees
90-56=34
======================================================
Explanation:
Refer to the diagram below. I've added the variable y as the base angles to the isosceles triangle on the left.
Recall that the angles opposite the congruent sides are the base angles. The base angles of any isosceles triangle are the same measure.
Let's solve for y
y+y+56 = 180 .... all angles in a triangle add to 180
2y+56 = 180
2y = 180-56
2y = 124
y = 124/2
y = 62
I've also added the variable z, which is adjacent to one of the y angles.
Since y and z combine to form a straight angle, this means the two angles add to 180
y+z = 180
z = 180-y
z = 180-62
z = 118
Now focus on the isosceles triangle on the right. It has angles x, x, and z = 118.
x+x+z = 180
x+x+118 = 180
2x+118 = 180
2x = 180-118
2x = 62
x = 62/2
x = 31
PLEASE ANSWER ASSAP!!!!!!!!!!!!!!!! WILL GIVE BRAINLEST!!!!!!!!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
i did this be for on my test
how do you solve this as a solution 9(2 + 3x) < 72
Answer:
x <2
Step-by-step explanation:
9(2 + 3x) < 72
Divide each side by 9
9/9 *(2 + 3x) < 72/9
2+3x < 8
Subtract 2 from each side
2+3x-2 < 8-2
3x<6
Divide each side by 3
3x/3 <6/3
x <2
What is 60.861 rounded to the nearest hundredth?
Answer:
60.900
Step-by-step explanation:
All of the zero's are optional, i feel safer putting them.
If a motorcycle is traveling at 5 m/s how long will take to travel 200 m/s
please help i'm really stuck on this! thank you :)
A crate has 272 red and green apples. How many green apples are there?
Answer:
149
Step-by-step explanation:
3 What is the greatest number which
divides 36, 42 and 45 exactly
without a remainder? ?
Answer:
3
Step-by-step explanation:
36 ÷ 3 = 12
42 ÷ 3 = 14
45 ÷ 3 = 15
yoko made $231 for 11 hours of work. At the same rate, how much would she make for 8 hours of work.
Answer:
Step-by-step explanation:
If Yoko made 231 dollars in 11 hours, it means that she makes
231/11=21 dollars per hour
in 8 hours
8*21=168 dollars in 8 hours
Answer:
168
Step-by-step explanation:
We need to find how much money she makes in one hour. Then multiply that by 8.
231 ÷ 11 = 21
21 × 8 = 168
Which soap deal has the lowest price per ounce?
$5.50 for 13.0 oz
$5.75 for 14.0 oz
$3.45 for 3.5 oz
$5.25 for 12.0 oz
Answer:
The 5.75 for 14.0 oz
Step-by-step explanation:
Hope this helps, Have an amazing day!!!
The length and width of a garden are in a ratio of 10:8. The perimeter of the garden is 324 feet. What is the length and width?
Answer:
length= 90feet
width =72 feet
Step-by-step explanation:
perimeter=2(L+W)
324=2(L+W)
324/2=L+W
162=L+W( at a ratio of 10:8)
length=10/18 * 162=90
width=8/18*162=72
2(90+72)=324
A veterinarian divided 1/3 of a bottle of medicine equally between 2 sick cats. How much did
he give each sick cat?
(7,1) and (-2,3)
Slope =
Answer:
The slope is [tex] - \frac{2}{9} [/tex].
Step-by-step explanation:
☆Remember:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
-
☆All we need to do is plug in!
[tex]m = \frac{3 - 1}{ - 2 - 7} = \frac{2}{ - 9} = - \frac{2}{9} [/tex]
The radius of a circle is 3.8 feet. Find the diameter.
Answer:
7.6ft
Step-by-step explanation:
Answer:
7.6
Step-by-step explanation:
3.8 + 3.8 = 7.6
The radius of a circle is half of the diameter
The radius is half of the circle length and the diameter is the whole length
remember that :)
Can somebody please help meee outt ???
Answer:
use formula of right angled triangle
Area=1/2b*p and DO YOURSELF
Step-by-step explanation:
LAZY GUY
Solve this system of equations using substitution:
y = 2r-4
x + 2y = 10
Step 1: Substitute for y in the second equation. Which is the
resulting equation?
Find the value of the expression
2 + z
for z = 16
Answer:
2+z= 18
Step-by-step explanation:
Since we know the value of Z is 16 all we have to do is take the z out and add a 16 there. So the problem would look like this. 2 + 16= 18
Jasmine makes an origami picture frame to display her favorite family photo. The size of the frame is 3.5 In by 8 in. What is the area of the frame?
Answer:
28 sq in
Step-by-step explanation:
Area =LxW
3.5x8=28
