Answer:
(a) 0.2033
(b) 0.0188
(c) 0.0004
(d) 0.095
Step-by-step explanation:
(a) the probability that a score at random is greater than 110 is obtained with a normal distribution of mean 100 and standard deviation 12 can be estimated using the z-table for Z = (110 - 100)/12 = 0.83
So P (X > 110) = P (Z > 0.83) = 0.2033
(b) Probability that a sample of 25 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{25} = 5[/tex]. That is a standard deviation of 12/5 = 2.4. which gives a Z-value of (105-100) / 2.4 = 2.08
P (X> 105) = P (Z > 2.08) = 0.0188
(c) Probability that a sample of 64 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard deviation reduced by a factor of [tex]\sqrt{64} = 8[/tex]. That is a standard deviation of 12/8 = 1.5. which gives a Z-value of (105-100) / 1.5 = 3.33
P (X> 105) = P (Z > 3.33) = 0.0004
(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105
This will be the addition of the two probabilities. We use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{16} = 4[/tex]. That is a standard deviation of 12/4 = 3. which gives us two different Z values to study:
(105-100) / 3 = 1.67
and for X= 95 ==> Z = (95 - 100)/3 = - 1.67
P (X > 105) = P (Z > 1.67) = 0.0475
P (X < 95) = P (Z < -1.67) = 0.0475
which add up to: 0.095.
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
b) 0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
c) 0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
d) 0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 100, hence [tex]\mu = 100[/tex].Standard deviation of 12, hence [tex]\sigma = 12[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{12}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
1 - 0.7967 = 0.2033
0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
Item b:
Sample of 25, hence [tex]n = 25, s = \frac{12}{\sqrt{25}} = 2.4[/tex].
This probability is 1 subtracted by the p-value of Z when X = 105, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{2.4}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812.
1 - 0.9812 = 0.0188
0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
Item c:
Sample of 64, hence [tex]n = 64, s = \frac{12}{\sqrt{64}} = 1.5[/tex].
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{1.5}[/tex]
[tex]Z = 3.33[/tex]
[tex]Z = 3.33[/tex] has a p-value of 0.9996.
1 - 0.9996 = 0.0004
0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
Item d:
Sample of 16, hence [tex]n = 16, s = \frac{12}{\sqrt{16}} = 3[/tex].
Both 105 and 95 are the same distance of the mean, so we find one probability, and multiply by 2.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
2 x 0.0475 = 0.095
0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
A similar problem is given at https://brainly.com/question/24663213
Alexander spent a total of 12.5 hours on a science project for the Science Fair. His sister, Laura, spent 16.6 hours on a science project. How many more hours did Laura spend on her project than Alexander spent on his?
Answer:
4.1 I think
Step-by-step explanation:
I just subtracted in my head
Answer:
4.1 hours
Step-by-step explanation:
Laura spent 4.1 more hours on her project than Alexander spent on his. If we split each number into 2 parts (like this: 12.5 -> 12 and .5; 16.6 -> 16 and .6) then we can subtract 12 from 16 and .5 from .6 to get 4 and .1. we add those together to get 4.1
(1 Point) : Solve the following inequality
for y.
10d – 2y <-6g
Answer:
[tex]y>3g+5d[/tex]
Step-by-step explanation:
Simplify the expressionA local construction site has workers that are digging the foundation of a new building. They
can haul away 20 lbs every 3.4 minutes while working. If they work for a total of 403
minutes, how many grams of dirt have they taken away? Round to a whole number.
Answer:
The workers can take away 1,075,280 grams of dirt in 403 minutes.
Step-by-step explanation:
[tex]\frac{403}{3.4}*20 = 2,370.588[/tex] pounds in 403 minutes
1 pound = 453.592 grams
2,370.588 * 453.592 = 1,075,280 grams
What is the meaning of the base of the function y= log(x)?
A. As y increases by 1, x increases by 10.
B. As y increases by 1, x increases by a factor of 10.
C. As y decreases by 1, x increases by a factor of 10.
D. As y decreases by 1, x increases by 10.
Please help! This is my last try at re-taking the test and I do not want to fail Math. :(
Answer:
184
Step-by-step explanation:
One ticket cost 23 (115/5)
23x8
Convert 144 pounds to kilograms. Use 1 kg = 2.2 Ib. Round your answer to the nearest tenth. kg
Answer:
Since 1 kg is equals to 2.2 lb. You divide 144 by 2.2 :
144/2.2
=65.45
=70 kg
where does 3.5 belong o the venn diagram
Answer:
I think i would be c or a but im not sure
step-by-step explanation:
what is the estimate product of 33 and 76
Represent the arithmetic series using the recursive formula. 94, 89, 84, 79, …
pLeAsE hUrRy
Answer:
The answer is 5
Step-by-step explanation:
Hope it helps <3 c:
how to get the answer to 3 1/2 ÷ 5 ( I need I step by step explanation :D )
Answer: .28
Step-by-step explanation: First turn the mixed number into an improper fraction. so 3x2+1=7, 7 is the the top and the bottom stays the same (2) so it would now be 7/2 divided by 5 which would equal .28
I hope this helps
The sum of two consecutive integers is 41. What are the two integers?
Answer:
Step-by-step explanation:
Let the smaller of two consecutive integer be x therefore other integer is x+ 1
As per statement the sum of two consecutive integers is 41. To find out the integers.
x + (x + 1) = 41
x + x + 1 = 41
2x + 1 = 41
2x = 41 - 1
2x = 40
x = 40/2
x = 20
The smaller of two consecutive integers is 20, thus other integer is x + 1 = 20 + 1 = 21
The two consecutive integers are 20 and 21
Answer the two consecutive integers are 20 and 21
Please help it’s due
4 = 130
2 = 50
1 = 90
3 = 40
:)
Evaluate 0 x 16).
6
-6
0
Answer:
0
Step-by-step explanation:
What are three consecutive even integers with the sum of -84?
Answer:
n will be -32
............... ....
PLEASE HELP!!! A line y=mx+b passes through point (−4, 6) and is perpendicular to y=−12x+6.
What is the value of b?
Answer:
Improper fraction: 19/3
Mixed number: 6 1/3
Step-by-step explanation:
If these two lines are perpendicular, their slopes are negative reciprocals of each other. The line would be something like:
y = (1/12)x+b
So plug in the coordinate values.
6 = (1/12)(-4)+b
6 = (-1/3)+b
6 1/3 = b
Out of 60 applicants to a university, 40 are from the East. If 20 applicants are to beselected at random, find the probability that:
a. 10 are from East.
b. Not more than 2 are from East.
Answer:
a. 40С10 * 20С10 / 60С20
b. 1 + (40)(20) + (40C2)(20C2) / 60С20
Step-by-step explanation:
Total number of application = 60
Total number of application from east = 40
Total number of application remaining = 20
Number of ways of selecting 20 applicant = 60C20 (Sample space)
a. Probability of 10 are from East.
= (10 from east) * (10 from remaining)
= 40С10 * 20С10 / 60С20
b. Probability of Not more than 2 are from East.
= P(x≤2)
= P(x=0) + P(X=1) + P(X=2)
= [40С0 * 20С20 / 60С20] + [40С1 * 20С19 / 60С20] + [40С2 * 20С18 / 60С20]
= 1 + (40)(20) + (40C2)(20C2) / 60С20
A snowplow has maximum speed of 45 miles per hour on a dry highway. Its maximum speed decreases by 1.6 miles per hour for every inch of snow on the highway. According to this model, at what snow depth will the snow plow be unable to move?
Answer:
28.125
Step-by-step explanation:
If it is going 45mph and every hour it decreases 1.6mph per inch of snow added. so 45 divided by 1.6 is 28.125.
The length of a rectangle is four times its width. Its perimeter is no greater than 170 cm. Find the greatest possible dimensions of the rectangle.
Step-by-step explanation:
let the length be =L
the width is 4 × the length
so the width will be 4L
the formular for the perimeter of a rectangle is =2(L +W)
170=2(L +4L)
170=2(5L)
170=10L
17=L
so the width is 4 × the length
17×4
=68
L=17
W=68
There are 24 first class seats and
192 coach class seats on an
airplane. If first class seats cost
$345 each and coach class seats
cost $228 each, find the total
revenue in ticket sales on a full
flight. NEED HELP ASAP THIS IS DUE AT 11:59
Answer:$52,056 I’m pretty sure
Step-by-step explanation:
WILL GIVE BRAINLIEST 20 POINTS!!! PLS HELP!!!?!?!?!?! DO NOT COPY AND PASTE FROM OTHER QUESTIONS OR I WILL REPORT U AND DELETE UR ANSWER!!!!
The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Jane's savings in dollars 3 9
f(x) = 3x + 3
Mariah's savings in dollars 6 9
Which statement best describes Jane's and Mariah's savings in the long run?
Jane will save more than Mariah.
Mariah will save more than Jane.
The savings will increase by the same factor for both.
The savings will increase by the same percentage for both.
Answer:
Mariah will save more than Jane.
Step-by-step explanation:
i think
Answer the following
Answer:
3x+2
Step-by-step explanation:
3(1)+2=5
3(2)+2=8
3(3)+2=11
A 180 pound person is hanging onto a 15-foot rope. Assuming the rope is uniform and that it weighs 2 pound per foot, set up (but do not evaluate) the integral that would calculate the work required to pull the person up 15 feet. Explain what of the values in your expression represent by labeling each.
Answer:
The answer is "g= 32 FPS"
Step-by-step explanation:
Given value:
[tex]mass = 180\\\\length= 15 \\\\\lambda = \frac{ mass}{ length} = 2 \ \text{pound per foot} \\\\\bold{Formula}\\\\ \to w \int_{a}^{b} F \cdot d \ dx = \int_{0}^{15} (2x+180) \ g \ dx[/tex]
by solving the value we get the value of g that is equal to 32.
PLEASE HELP ME! THANK YOU!
Answer:
PICTURE NOT LOADING BUT GUESS OR LOOK IT UP OR SOMETHING SORRY SOS ANYONE SOS
Step-by-step explanation:
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. Complete this sentence: The rate for Printer B is (a) ____________ the rate for Printer A because the rate of 25 pages per minute is (b) _____________ the rate of (c) __________ pages per minute for Printer A.
Answer:
a equal to c 25 b greater than
Step-by-step explanation:
Answer:
As per graph the rate of Printer A is 15 pages per minute.
Missing words are:
(a) greater than(b) greater than(c) 15The rate for Printer B is greater than the rate for Printer A because the rate of 25 pages per minute is greater than the rate of 15 pages per minute for Printer A.
For every left-handed person, there are about 4-right handed people. If there are 30 students in a class, predict the number of students who are right-handed.
Answer:
There are 24 right handed students
Step-by-step explanation:
This is a ratio question so it would be represented as 1:4.
First you would do 1 + 4 which is 5.
Then do 30 ÷ 5 which is 6.
Finally multiply 6 by 4 and 1.
So 6 × 4 × 1 is 24.
So there are 24 students who are right handed.
Hope this makes sense!
PLZZZZ ANSWER FAST. THANK YOU!
Answer:
3 ounces of water
Step-by-step explanation:
Ratios are equivalent:
6:4 is equivalent to 3:2
14) At a school 5/8 of the teachers are male
There are 72 teachers
work out how many teachers are female
Answer:
45
Step-by-step explanation:
72 ÷ 8 = 9. Every 9 teachers is [tex]\frac{1}{8}[/tex]. Since there are [tex]\frac{5}{8}[/tex]teachers that are male, 9 x 5 = 45 female teachers, which leaves 25 male as well
hope this helped
Describe two differences in the atomic structure of nitinol and the atomic structure of either nickel or titanium that result in different physical properties of the elements used to make nitinol. CAN ANYONE HELP, PLEASE!!!!
Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
What is nitinol?Nitinol is an alloy containing an equal quantity of elements of nickel and titanium.
It is a superelastic alloy and has shape memory capacity.
It retains its shape after reforming into another shape by an increase in temperature.
Thus, the difference is that Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
Learn more about nitinol
https://brainly.com/question/8028003
2/4=13/x ( need help on this to
Answer:
x=6.5
Step-by-step explanation:
Cross multiply
4x=26
Divide 26/4 ( 6.5 )
x=6.5
Slope for (20,8)(9,16)?
Answer:
m=-8/11
Step-by-step explanation:
[tex]\frac{Y2-Y1}{X2-X1} =\frac{y}{x}[/tex]
[tex]\frac{16-8}{9-20} =\frac{-8}{11}[/tex]
