Answer:
a) [tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
b) The 95th percentile is 4.4935 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 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.
The reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours.
This means that [tex]\mu = 4, \sigma = 1.2[/tex]
16 reviews.
This means that [tex]n = 16, s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
This is the pvalue of Z when X = 4.25 subtracted by the pvalue of Z when X = 3.5. So
X = 4.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.25 - 4}{0.3}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a pvalue of 0.7967
X = 3.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.5 - 4}{0.3}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a pvalue of 0.0475
0.7967 - 0.0475 = 0.7492
So
[tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
C. Find the 95th percentile for the mean time to complete one month's reviews.
This is X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 4}{0.3}[/tex]
[tex]X - 4 = 0.3*1.645[/tex]
[tex]X = 4.4935[/tex]
The 95th percentile is 4.4935 hours.
I need help on this 1+s=3
Answer:
s = 2
Step-by-step explanation:
3 - 1 = 2
1 + 2 = 3
Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
giving brainliest!!
pls help asap *easy*
Answer:
V ≈ 16.333 in³
Step-by-step explanation:
Formula of the Volume of a Sphere: [tex]\frac{4}{3} \pi r^{2}[/tex]
V = [tex]\frac{4}{3}[/tex] × (3.5)²π
V = [tex]\frac{4}{3}[/tex] × 12.25π
V ≈ 16.333 in³
Calculator
13 in
94
7.5 in.
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest tenth.
Answer:
9165.0
Step-by-step explanation:
13*94*7.5 = 9165.0
Find the surface area of a basketball with a diameter of 10 in.
400π in²
10π in²
100π in²
25π in²
Answer:
100 pie
Step-by-step explanation:
Find the surface area of a basketball with a diameter of 10 in.
100π in²
10π in²
400π in²
25π in²
The surface area of the basketball is 100π square inches.
The correct option is C.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The shape of the basketball is spherical.
The diameter of the basketball is 10 inches.
So, the radius of the basketball = 10/2 = 5 inches.
The surface area of the basketball,
= the surface area of the sphere.
= 4πr²
= 4π(5)²
= 2π25
= 4 x 25π
= 100π square inches.
Therefore, the surface area is 100π square inches.
To learn more about the surface area of the sphere;
https://brainly.com/question/14692728
#SPJ6
Find the difference.7/14−3/14= help
Answer: [tex]\frac{4}{14}[/tex]
Step-by-step explanation:
Let's take the given equation
[tex]\frac{7}{14}-\frac{3}{14}[/tex]
Let's also remember the bottom number (denominator) does not change or go away ever!
So we will subtract the top numbers (numerator) and we will get
[tex]\frac{4}{14}[/tex]
At Chill Hill, there are 540 ways to make an ice cream sundae consisting of one flavor ice cream, one topping, and one type of syrup. If there are 9 ice cream flavors and 5 types of syrup, how many toppings are there?
Please explain for brainliest.
Answer:
12 toppings
Step-by-step explanation:
9x5=45
540/45=12
a solution set always include....
A solution is any value of a variable that makes the specified equation true. A solution set is the set of all variables that makes the equation true. ... If the two sides are equal, the equation is true and thus the value is a solution.
Given: c=58, b=15, angle B=15 degrees a= ?
a. 60
b. 52
c. 56
Answer:
c. 56
Step-by-step explanation:
To Find a= it would be opposite of angle A.
We could use trig ratios for this question.
Cos B= a/c
Cos 15= a/58
a = (cos15)(58)
a=56
Select the correct answer from each drop-down menu.
A camp director developed the function m(c) = 12c + 80 to model the total cost of taking c campers on a field trip to the movies.
In the camp director’s function, the number of campers is the _______ variable and the total cost of the trip _________
1. ( independent, dependent )
2. ( changes by a constant factor per camper, Changes by a constant amount per camper )
.
Answer:
(a) Independent variable
(b) The constant factor is 12
Step-by-step explanation:
Given
[tex]m(c) = 12c + 80[/tex]
c = campers
m = total cost
Solving (a) What type of variable is the number of campers (c)
The total cost (m) is dependent on the number of campers (c) for its own value.
In other words, if c changes from 5 to say 7, the value of m will also change.
This implies that the number of campers is an Independent variable
Solving (b): Constant factor
This in other words means, rate of change (or slope)
A linear function is:
[tex]y = ax + b[/tex]
Where a represents the slope
By comparison with: [tex]m(c) = 12c + 80[/tex]
Hence, the constant factor is 12
Answer:
dependent, changes by a constant factor per camper.
Step-by-step explanation:
Please Help! I'll give thanks and best rate if its correct! (type link into another tab)
Answer:
x = 8
Step-by-step explanation:
Answer:
sorry bro I would but that link is super long
Step-by-step explanation:
thats what she said
someone please help thanks
Answer:
Don't take my word for it because I havent dont this in a while but I believe it is the top right
Please help if not that’s fine no nonsense
Answer:
B) 54 and 54
Step-by-step explanation:
72 + x + x = 180
2x + 72 = 180
2x = 180 - 72
2x = 108
x = 54
Solve the proportion.
10
15
a
24
a = [?]
help please I will give you brainliest!!
Let's solve your equation step-by-step.
10/a=15/24
Step 1: Cross-multiply.
10/a=15/24
(10)*(24)=15*a
240=15a
Step 2: Flip the equation.
15a=240
Step 3: Divide both sides by 15.
15a / 15 = 240/15
a=16
ik this is alot but please help me.
Answer:
help u in what please ask the question so we can anwser
Graph a line with the given slope that passed through the given point.
slope: 0, point: (0, -2)
Answer:
Graph the line y = -2.
Step-by-step explanation:
A line with zero slope is a horizontal line. Find (0, -2) on the y-axis and draw a horizontal line through it. This will fully address this question.
Which angle measure is a complement of an angle whose measure is 62 degrees?
A 96
B 118
C 16
D 28
angle measure is a complement of an angle whose measure is 62 degrees=90-62=28.
Answer:
D 28 is your answer
A rectangular poster has an area of 26 square feet. It is 4 1/3 feet wide at it's base. What is the height of the poster?
Answer:
6 square feet
Step-by-step explanation:
Area = L * w
26 = L * 4 1/3
26 = L * 13/3
L = 26 divided by 13/3
L = 26 * 3/13 = 6
answer = 6
someone help me!! i’ll mark brain list!!
In deenas class, 3/12 of the students voted for cats as their favorite pet, and 5/12 voted for dogs. What fraction of the class voted for cats or dogs as their favorite pet?
Answer:
8/12 or 2/3
Step-by-step explanation:
5/12+3/12=8/12
8/12 simplifies to 2/3
PLS HELP ME ASAPPP!!!!
Answer:f is the answer
Step-by-step explanation:
Hoshi walks 10 meters in 3 seconds. She walks the same at this rate for 50 seconds. How far does she walk?
I give brainalist and points for an answer and explanation
Answer:
option D
Step-by-step explanation:
diameter of two small circle i.e 14cm
radius of two small circle =7cm
area of the small circle =πr²
area of the small circle=22/7 x7²
area of the small circle=154cm²
Radius of bigger circle =14cmArea of bigger circle=πr²Area of bigger circle=22/7×14²
Area of bigger circle=616cm²
Area of shaded region =area of bigger circle -area of small circle +area of small circle
area of shaded region =616-154+154
area of shaded region=308cm²
i.e approximately 282.74cm²
I’ll give points and brainalist for correct answer / explanation
Answer:
i think you forgot to attach the image lol
Step-by-step explanation:
In a particular library, 18% of the books are children's books, 53% of the books are adult fiction, and the rest are adult nonfiction. You select 3 books at random; what is the probability That none of them are children's books?
Answer:
3321 / 12500
Step-by-step explanation:
P (not child, not child, not child) = 82/100 × 81/100 × 80/100
Help please I give brainliest serious plz
Answer:
brainlisdt pplease
Step-by-step explanation:
please help me thanks.
Answer:
I hope this helps you
Step-by-step explanation:
1/8 ÷ 3 = 1/8 × 1/3
= 1/24
= 0.0416666667
I am having trouble with this question, can someone help i labed them 1,2,3, and 4.
Answer:
3
Step-by-step explanation:
because if he turns right 90 he will get to school but if he turns left 90 he might get half way to the golf course. And since it doesn't specify there is no way in knowing which way to turn
A television station shows 3 commercials every 12 minutes. At this rate, how many commercials will the station show in 84 minutes?
Answer:
21
Step-by-step explanation:
84/12=7x3=21
Which of the following is in the solution set to 3x - y = 12? (hint: what
makes the equation true)
(3,2)
(0,4)
(-4,0)
(8,12)
Answer(8,12)
Which set of numbers shows the lower extreme, the lower quartile, the median, the upper quartile, and the upper
extreme for the box-and-whisker plot shown?
(14, 13, 28, 45, 54)
(6,12, 28, 44, 54)
(12, 20, 28, 44, 54)
Will give brainly
Please help me
(6,19,27, 44,54)
B: (6,12,18,44,54)
I just did this and this was correct.
Answer:option B
Step-by-step explanation:i got it right trust me
