Answer:
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
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 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.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Standard deviation of 2 and a mean diameter of 200 inches.
This means that [tex]\sigma = 2, \mu = 200[/tex]
83 shafts
This means that [tex]n = 83, s = \frac{2}{\sqrt{83}}[/tex]
What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches?
Mean between 200 - 0.2 = 199.8 inches and 200 + 0.2 = 200.2 inches, which is the p-value of Z when X = 200.2 subtracted by the p-value of Z when X = 199.8.
X = 200.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{200.2 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = 0.91[/tex]
[tex]Z = 0.91[/tex] has a p-value of 0.8186
X = 199.8
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{199.8 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = -0.91[/tex]
[tex]Z = -0.91[/tex] has a p-value of 0.1814
0.8186 - 0.1814 = 0.6372
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
The circumference of the base of the cone is 8.5 inches. What is the volume of the cone in term of pi? Round to the nearest hundredth
========================================================
Work Shown:
C = 2*pi*r ......... circumference of the circular base
r = C/(2pi)
r = (8.5)/(2pi)
r = 4.25/pi
-------------
V = pi*r^2*h ...... volume of the cone
V = pi*(4.25/pi)^2*15
V = pi*(18.0625/pi^2)*15
V = (18.0625*15)/pi
V = 270.9375/pi ..... exact volume in terms of pi
If we round that decimal number up top to the nearest hundredth, then we end up with V = 270.94/pi
If a total of 360 students were involved in the evening's activities, how many students attend the school?
Intersection and conditional probability problem. Can anyone help solve this problem?
Part (a)
Refer to figure 1 in the attached image below. The a,b,c,d,e are placeholders for numbers we'll fill in later (that turns into the table for figure 2). Hopefully you agree about the placement of the numbers. If there's any confusion, then please let me know.
Along the bottom row, we can see that 39+e = 65 which solves to e = 26 after you subtract 39 from both sides. This tells us that there are 26 non-physics majors (ie their major is anything but physics).
Then along the "non-physics" column, notice how b+6 = e, which is the same as b+6 = 26 after replacing 'e' with 26. Solving that equation leads to b = 20. So we have 20 people who are seniors and non-physics majors.
Now move to the top row. We can see that a+b = 30, which is the same as a+20 = 30 because we plug in b = 20. That solves to a = 10. So we have 10 seniors who are physics majors.
----------------
Now along the first column, we have a+c = 39, aka 10+c = 39, which solves to c = 29. There are 29 non-seniors who are physics majors.
The last variable to find is variable d.
Along the second row, we can say,
c+6 = d
29+6 = d
d = 35
Or we could say that 30+d = 65 along the last column which also solves to d = 35. This tells us we have 35 non-seniors in the class.
----------------
To summarize so far, we have
a = 10, b = 20, c = 29, d = 35, e = 26
These values will replace the letters as shown in figure 2.
Figure 2 will be used to answer both parts (a) and (b).
----------------
After that (more than) slight detour of filling in the table, we can finally tackle the question at hand. We're asked to find the probability of selecting someone who is a senior and a physics major. We have a = 10 people who fit the description out of 65 total
Divide the two values and reduce the fraction as much as possible
10/65 = (2*5)/(13*5) = 2/13
Answer: 2/13==========================================================
Part (b)
There's a lot going on with part (a). Luckily there aren't many steps here because pretty much all the work has been done already. We'll refer to figure 2 below.
We're told "given the student is a physics major", which means we focus solely on the "physics major" column only. We ignore everyone else because we know 100% that whoever we selected majored in physics.
We have a = 10 seniors who are also physics majors out of 39 physics majors total.
That constructs the fraction 10/39
Answer: 10/39ASSESSMENT:
Act as the person in the problem Do the activity. Record your
findings then answer
1. A farmer placed 250 mangoes in a crate, these are 150 ripe and 100 unripe
mangoes, his wife randomly selected 80 mangoes, she got 50 ripe mangoes
and 20 unripe mangoes, find the experimental probability of the mangoes she
selected.
2. A table tennis player has 40 orange table tennis balls, 30 white and 20 yellow
table tennis balls. After selecting 18 balls, he found out that he got 6 white
table tennis balls. Find out the experimental probability of getting white table
tennis table tennis balls.
please answer this
Answer:
in 1st his wife selected 80 mangoes 50 ripe and 20 unripe how it can be
Step-by-step explanation:
50+20=70 not 80
please share the correct question than I may help you
(x-7)(x^2+3x-3) multiply the polynomials
Step-by-step explanation:
= (x - 7)(x² + 3x - 3)
= x³ - 7x² + 3x² - 21x - 3x + 21
= x³ - 4x² - 24x + 21
Use substitution to solve the system of equations and choose the solution from the list below.
Look at the image
Answer:
Option : ( 2 , 6 )
x = 2, y = 6
Step-by-step explanation:
[tex]y = 4x - 2[/tex] ---------------- ( 1 )
[tex]y = -2x + 10[/tex] -------------- ( 2 )
Substitution Method
Substitute ( 1 ) in ( 2 ) :
[tex]4x - 2 = -2x + 10\\\\4x + 2x = 10 + 2\\\\6x = 12\\\\x = 2[/tex]
Now substitute x in ( 2 ):
[tex]y = -2x + 10\\\\y = -2 ( 2 ) + 10\\\\y = - 4 + 10 \\\\y = 6[/tex]
7) -4 = 2(b + 5)
please help!
Answer:
b = -7
Step-by-step explanation:
Let's solve your equation step-by-step.
−4 = 2(b + 5)
Step 1: Simplify both sides of the equation.
−4 = 2(b + 5)
−4 = (2)(b) + (2)(5)(Distribute)
−4 = 2b + 10
Step 2: Flip the equation.
2b + 10 = −4
Step 3: Subtract 10 from both sides.
2b + 10 − 10 = −4 − 10
2b = −14
Step 4: Divide both sides by 2.
[tex]\frac{2b}{2} = \frac{-14}{2}[/tex]
b = -7
Hope this helps, please mark brainliest if possible. Have a great day! :)
What is the solution of the equation x2 + 4x + 10 = 0?
Answer:
The answer for thid equation is x = -5/3
Andy's average driving speed for a 4 hour trip was 48 miles per hour. During the first 3 hours he drove 50 miles per hour. What was his average speed for the last hour on his trip.
PLEASE HELP AND SHOW WORK YOU WILL GET BRAINLEST MARK
Answer:
Step-by-step explanation:
Distance = 48 * 4
Distance = 192
~~~~~~~~~~~~~~~
3*50 = 150
192 - 150 = 42
42 MPH for the last hour
The population of a rabbit colony triples each month.
The population started with 5 rabbits. How many
rabbits are there after 6 months?
Answer:
3645 rabbits after 6 months.
Step-by-step explanation:
The population of a rabbit colony triples each month.
This means that the population of the colony after t months is given by:
[tex]P(t) = P(0)(3)^t[/tex]
In which P(0) is the initial population.
The population started with 5 rabbits.
This means that [tex]P(0) = 5[/tex]
So
[tex]P(t) = 5(3)^t[/tex]
How many rabbits are there after 6 months?
This is P(6). So
[tex]P(6) = 5(3)^6 = 3645[/tex]
3645 rabbits after 6 months.
at the present time, gerald is eight less than five times his nephews age. seven years ago gerald was 9 times his nephews age.
(A)if g represents geralds age now and n represents his nephews age today. use a system of equations that could be used to model this scenario?
(B)than use the equations to determine algebraically the ages of both Gerald and his nephew.
(C)than determine in how many years Gerald will be three times as old as his nephew?
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean, ayy
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean
Select the correct answer.
Given: ΔABC
Prove: The sum of the interior angle measures of ΔABC is 180°.
Answer:
C
Step-by-step explanation:
When ever a problem gives information about parallel lines, look for Alternate Interior angles.
Answer:
A
Step-by-step explanation:
(») Evaluate the expression.
* * (4 + 8)
Answer:
6
Step-by-step explanation:
work out the brackets first....4+8=12
the multiply 1/2 by 12
1/2 x 12 = 6
PLS HELP I WILL GIVE BRAINLIEST
Answer:
80°
Step-by-step explanation:
So as you can see, the givin angle is 100°. So that must mean that angle DBF is 80° because they are supplementary angles. (Together they equal 180°) And sense the pair of lines are parallel, and x is the smaller angle so it is 80°.
Divide the following two complex numbers.
3+2i
5-3i
Step-by-step explanation & answer:
Conjugate = 5+3i
Multiply fraction by conjugate:
(15+9i+10i+6i^2) / (25-9i^2)
Simplify:
(15+19i+6i^2) / (25-9i^2)
i^2 is -1:
(15+19i-6) / (25+9)
So:
9+19i / 34
Into a +bi form:
9/34 + 19i/34
Celeste is planning to buy a new bedroom set. Because sales tax rates can vary from town to town,
Celeste wants to compare the sales tax rates at two retail locations before making the purchase.
The price of the new bedroom set that Celeste wants to buy is $2,734. The sales tax rates in the
two cities at the time of purchase are given in the table.
9514 1404 393
Answer:
$13.67, Valdosta, Tallahassee
Step-by-step explanation:
The total sales tax rate in Valdosta is 4% +3% = 7%.
The total sales tax rate in Tallahassee is 6% +1.5% = 7.5%, which is 0.5% higher than in Valdosta. That percentage makes a difference in the final price of ...
0.5% × $2734 = 0.005×$2734 = $13.67
Celeste will save $13.67 in sales tax if she makes her purchase in Valdosta rather than Tallahassee .
What is the volume of the cone? Use 3.14 for π
Answer:
What is the height, radius or diameter of the cone?????
Find the value of x.
Plz help :/
Answer:
10
Step-by-step explanat
ion:
Yes i give brainliest
Selena Gomez is running the Gary Mintz Marathon. After 6 miles, Selena Gomez's clock reads 48 minutes. If Selena Gomez maintains her current pace, what will her clock read at 20 miles? You can use the table below to calculate her times.
A : 56
B: 160
C: 140
D: 96
Answer:
The answer would be C: 140.
Un ganadero está reparando una mezcla de avena y harina de maíz para ganado. Cada onza de avena proporciona 4 gramos de proteína y 18 gramos de carbohidrato; una onza de harina de maíz proporciona 3 gramos de proteína y 24 gramos de carbohidratos.
¿Cuántas onzas de cada uno se pueden usar para satisfacer las metas nutricionales de 200 gramos de proteína y 1320 gramos de carbohidrato por ración?
Answer:i love you
Step-by-step explanation:
don’t understand this help please
Step-by-step explanation:
Since he sold $70,834 worth of cars, he earned an extra 5% commission on the sale. That means he got
0.05×($70,834) = $3,541.70
Therefore, his salary for the month m is
m = $2250 + 0.05s = $2,250 + $3,541.70 = $5,791.70
The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides
Answer:
???
Step-by-step explanation:
Of all the calls in the first quarter of year 5, how many were abandoned
I do not know what you mean, but ok.
2x-4=20
Please fast with steps !
Answer:
x=12
hope it will helpful to you
Seema is travelling to Guernsey. She travels a distance of 3,800 km by plane to London and then another 400 km to Guernsey. Both planes fly at an average speed of 900 kmh-1.
What is her total flight time in hours and minutes, to the nearest minute?
9514 1404 393
Answer:
4 hours 40 minutes
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
time = (3800 km)/(900 km/h) +(400 km)/(900 km/h) = (38+4)/9 h
= 14/3 h = 4 2/3 h
Seema's flight time is 4 hours 40 minutes.
__
2/3 of 60 minutes is 40 minutes
Hãy giải giúp tôi câu tính giới hạn này
Answer:
Step-by-step explanation:
What are the center and radius of the circle defined by the equation x^2 + y^2 -6x + 8y + 21=0
Answer:
Step-by-step explanation:
(x²-6x)+(y²+8y)=-21
(x²-6x+9)+(y²+8y+16)=-21+9+16
(x-3)²+(y+4)²=4
center=(3,-4),radius=√4=2
How much will you have if : S900 invested at 6% compounded semiannually
for 5 years.
Answer:
Step-by-step explanation:
A = P(1+r/n)^nt
A = 900(1 + .06/2)^(5*2)
A = 900(1.03)^10
A=1209.52
Which of the following is an example of data organization?
A. administering questionnaires
B. calculating a standard deviation
c. representing data with a histogram
D. declaring a statistically significant difference between groups
c) representing data with a histogram is an example of data organization