Answer:
0.2643 = 26.43% probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors.
Step-by-step explanation:
To solve this question, we need to understand the normal distribution, the central limit theorem, and subtraction of normal variables.
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.
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]
Subtraction of normal variables:
When we subtract normal variables, the mean of the subtraction will be the subtraction of the means, while the standard deviation will be the square root of the sum of the variances.
In a large local high school, 19% of freshmen have had their wisdom teeth removed. Sample of 60 freshmen:
So, by the central limit theorem:
[tex]\mu_f = 0.19, s_f = \sqrt{\frac{0.19*0.81}{60}} = 0.0506[/tex]
24% of seniors have had their wisdom teeth removed. Sample of 50 seniors.
So, by the central limit theorem:
[tex]\mu_s = 0.24, s_s = \sqrt{\frac{0.24*0.76}{50}} = 0.0604[/tex]
What is the probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors?
This is the probability that the subtraction of the proportion of freshmen by the proportion of seniors is larger than 0. For this distribution, we have that:
[tex]\mu = \mu_f - \mu_s = 0.19 - 0.24 = -0.05[/tex]
[tex]s = \sqrt{s_f^2 + s_s^2} = \sqrt{0.0506^2 + 0.0604^2} = 0.0788[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0 - (-0.05)}{0.0788}[/tex]
[tex]Z = 0.63[/tex]
[tex]Z = 0.63[/tex] has a pvalue of 0.7357
1 - 0.7357 = 0.2643
0.2643 = 26.43% probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors.
Answer
I got 0.263 and was correct.
Step-by-step explanation:
Edge 2022
Samantha invests $11,000 at 10% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answer:
12100
Step-by-step explanation:
I = PRT
plug in the numbers and don't forget you need to add the first number again
I = 11000 × .10 × 1 + 11000
The organizers of a convention are drawing lots to pick the host city for the event. Nine city names are written on different
pieces of paper and placed in a bowl. The possible outcomes of drawing a name from the bowl are shown below.
Chicago
Seattle
Orlando
Dallas
Atlanta
Austin
Oakland
Phoenix
Cleveland
What is the probability that Cleveland or Dallas is picked?
OA.
OB.
OC.
DIN COIN
OD
Answer:
2/9
Step-by-step explanation:
each city has a probability of 1/9
one city 'or' another means to add their probabilities: 1/9 + 1/9 = 2/9
The probability of Cleveland or Dallas getting picked is [tex]\frac{2}{9}[/tex].
What is probability?'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'
According to the given problem,
Total number of city names = 9
Favorable events = 2 [ Cleveland, Dallas]
Probability = [tex]\frac{Favorable events}{Total number of events}[/tex]
Probability of Cleveland getting picked = [tex]\frac{1}{9}[/tex]
Probability of Dallas getting picked = [tex]\frac{1}{9}[/tex]
Probability of Cleveland OR Dallas getting picked = [tex]\frac{1}{9}+\frac{1}{9}[/tex]
= [tex]\frac{2}{9}[/tex]
Hence, we can conclude, probability of Cleveland or Dallas getting picked is [tex]\frac{2}{9}[/tex].
Learn more about probability here: https://brainly.com/question/11234923
#SPJ2
How much would you need to deposit in an account now in order to have $2000 in the account in 10 years!
Assume the account earns 7% interest compounded monthly
Answer:
$2000
Step-by-step explanation:
they gotta take the first bunch then the next
A television sells for $700. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $200 down and $50 a month for
14 months. How much is saved by paying the total amount at the time of the purchase?
find the area and perimeter of a 30-gon with a radius of 1
Answer:
Here :D
Step-by-step explanation:
look at one of the 30 central triangles.
Each will be isosceles with a vertex angle of 12°
base^2 = 1^2 + 1^2 - 2(1)(1)cos12°
= 2 - 2cos12°
so the perimeter is 30(2 - 2cos12°)
= 60 - 60cos12°
use your calculator if you need a decimal answer.
Help please 60 points who ever gets it right gets Brainliest
Answer:
B
Step-by-step explanation:
Daniel and Hector both throw shot put for their school's track and field team.
They each threw 5 times and recorded their distances to the nearest foot.
Daniel's Shot Put Throws (feet)
27, 30, 34, 35, 34
Hector's Shot Put Throws (feet)
38, 24, 38, 40, 35
Who has the greater mean, and by how much?
А Daniel by 3 feet
B Hector by 3 feet
С Daniel by 6 feet
D Hector by 6 feet
Answer:
Option B : Hector by 3 feet is the correct answer.
Step-by-step explanation:
Given that:
Mean of Daniel = [tex]\frac{Sum\ of\ quantities}{Number\ of\ quantities}[/tex]
Mean of Daniel = [tex]\frac{27+30+34+35+34}{5} = \frac{160}{5}[/tex]
Mean of Daniel = 32 feet
Mean of Hector = [tex]\frac{38+24+38+40+35}{5} = \frac{175}{5}[/tex]
Mean of Hector = 35 feet
Therefore,
Hector has a greater mean
Difference = Hector's Mean - Daniel's Mean
Difference = 35 - 32
Difference = 3 feet
Hence,
Option B : Hector by 3 feet is the correct answer.
Your local pizza store sells medium pizzas for $7.79 each, and breadsticks for $2.49 per order. For a party, you decide to order 5 pizzas and 2 orders of breadsticks. There is a $2 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax
Answer:
The total bill after tax will be of $50.06.
Step-by-step explanation:
Total cost:
5 pizzas, each for $7.79
2 orders of breadsticks, each for $2.49
$2 delivery fee.
9.4% sales tax.
What will be the total bill after tax
[tex]T = 5*7.79 + 2*2.49 + 0.094*(5*7.79 + 2*2.49) + 2 = 50.06[/tex]
The total bill after tax will be of $50.06.
find the compound interest when principal =2000 rate =20%per annum and time 3 years
⇒[tex] A = P (1 + \dfrac{R}{100} )^{n}[/tex]
=[tex]2000 (1 + \dfrac{20}{100})^{3}[/tex]
= [tex]2000 ( 1 + \dfrac{1}{5} )^{3}[/tex]
= [tex]2000 (\dfrac{6}{5}) ^{3}[/tex]
= [tex]2000 \times\dfrac{6}{5} \times \dfrac{6}{5} \times \dfrac{6}{5}[/tex]
= 16 × 6 × 6 × 6
⇒A = Rs.3456
⇒CI = A - P
⇒CI = 3456 - 2000
⇒CI = Rs.1456
Answer:-
·Compound interest is Rs.1456.
PLS ANSWER ASAP: 5/8 divided by 3/4 also 3 divided by 3/4.
Answer:
1- 5/6 or 0.83 with the 3 repeating
2- 4
Step-by-step explanation:
Hope this helps
How much is 645 divided by 5
Step-by-step explanation:
129
hope it helps
please mark me as brainlist
Answer:
it is 129
Step-by-step explanation:
Please help meee
Determine if the two triangles are congruent. If so, give the reason, if not, write "Not Congruent".
Answer:
its congruent because of the lines
Need answers ASAP! TYSM in advanced!
Answer:
The answer is KLM, I hope it helped
Step-by-step explanation:
I got that answer because going in that order, the numbers are similar/ the same
What is it ? Plzzzzzzzzz help
in this ...
180-142 =38
38 is the correct answer
question: solve for x.
please someone help!
by angle sum property of triangle,
70+60+(x+60)=180
=> 190 +x = 180
=> x = 180-190
=> x = -10
Plzzzzzzzzzz Hurry I will mark brainliest if you get it right
solve for m: 20≤ m/5+12
A. -40>m
B. 40 ≥ m
C. 40 ≤ m
D. -40 < m
Answer: C
Step-by-step explanation:
40/5 =8
20≤8+12
20≤20
What is the ratio of the circumference of a circle to the diameter called?
рі
area
chord
radius
Answer:
pi
Step-by-step explanation:
3.
× 4.76
3.36
plss help me
Point Jis located at -28 on a number line and point kis located at -3.
What is the midpoint between Jand K?
A. 40
B.-15.5
C.-4.8
D.-17.5
Help me out here pleaseeeeeeeee
Answer: 5 pounds
Step-by-step explanation:
Think about it in order to find j you multiply 6 times c. If j=30 you divide 30 from 6 to find the value of c. This is why c is 5.
Hope this helps :)
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
$$
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 1 over 4 end fraction comma 3 over 8 end fraction right parenthesis.
Step-by-step explanation:
what u suppose to do on this work, reply quickly so I can help
Answer:
3/2
Step-by-step explanation:
A proportional relationship is described by ...
y = kx
The value of k can be found by dividing by x:
k = y/x
For the given non-zero point (1/4, 3/8), the value of k is found to be ...
k = (3/8)/(1/4) = (3/8)/(2/8)
k = 3/2
The constant of proportionality is 3/2.
the proportion of brown M&M's in a milk chocolate packet is approximately 14%
Answer: chocky milk
Step-by-step explanation: chocky milk make pain go away
Which relationships have the same constant of proportionality between y and x as the following table.
x = 2, 7, 9
y = 7, 24.5, 31.5
Choose three answers
A. 4y = 14x
B. 3.5y = x
C,D,E look at the picture for
Answer:
A, D, E
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Factor the expression. d2 + 10d + 25
Answer:
(d+5)^2
Step-by-step explanation:
1.
Here are two rectangles.
Not to scale
71 cm
63 cm
48 cm
56 cm
I
Are the rectangles mathematically similar?
Show your reasoning
Answer:
no it is not.two side must be equal in rectangle.
how do i convert from degrees to radians in terms of pi?
Answer:
Formula
1° × π/180 = 0.01745rad
Step-by-step explanation:
Answer:
there are 2 ways.
Step-by-step explanation:
1st way multiply the degree with π÷180
2nd way D/90=2C/π [where D refers to Degree and C refers to Radians ]
The sum of two numbers is 57 . The smaller number is 17 less than the larger number. What are the numbers?
Answer:
two numbers are 37 and 20
Step-by-step explanation:
x+y=57
let x be the smaller number
y=x+17
x + x+17=57
2x=57-17
2x=40
x=20
y=x +17
y=20+17
y=37
50, 20, 8, ...
Find the 8th term.
Answer:
0.08192
Step-by-step explanation:
Given 50, 20, 8, ...
The sequence is geometric in nature
The nth term of the geometric sequence is exoressed as;
Tn = ar^{n-1}
a is the first term = 50
r is the common ratio = 20/50 = 8/20 = 2/5
n is the number of term = 8 (since we need the 8th term)
Substitute
T8 = 50(2/5)^{8-1}
T8 = 50(2/5)^7
T8 = 50(128/78,125)
T8 = 0.08192
Hence the 8th term is 0.08192
is ( -1,5 ) a solution to the equation 2x+5y=0 Why or Why not?
Answer:
No, that is not a solution
Step-by-step explanation:
Plug in the numbers to their respective values, so -1 to x, and 5 to y.
2(-1) + 5(5) = 0
-2 + 25 = 0
23 = 0?
No, that is not a solution
Christina loses 2 1/2 pounds every month for a year. How much weight did she lose that year? There are 12 months in a year. Simplify (or reduce) your answer, if necessary.
Answer:
30 pounds
Step-by-step explanation:
So for this problem you do 2 1/2 * 12, or 5/2 * 12. You get 60/2 = 30.
Answer:
30 pounds
Step-by-step explanation:
We start by converting 2 1/2 pounds into its decimal form: 2.5 pounds.
Now we consider that there are 12months per year, therefore in one year she will lose:
2.5 * 12 = 30 pounds