Answer:
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem and difference between normal variables.
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 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.
Subtraction of normal sample means:
When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.
Sample size of 55 men with mean 785 and standard deviation 489
This means that:
[tex]\mu_A = 785[/tex]
[tex]s_A = \frac{489}{\sqrt{55}} = 65.9367[/tex]
Sample size of 40 women with mean 670 and standard deviation of 419
This means that:
[tex]\mu_B = 670[/tex]
[tex]s_B = \frac{419}{\sqrt{40}} = 66.2497[/tex]
Difference between sample means:
The mean and the standard deviation are, respectively:
[tex]\mu = \mu_A - \mu_B = 785 - 670 = 115[/tex]
[tex]\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47[/tex]
What is the probability of obtaining a difference between sample means of 110 mg or more?
This is 1 subtracted by the pvalue of Z when X = 110. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 115}{93.47}[/tex]
[tex]Z = -0.053[/tex]
[tex]Z = -0.053[/tex] has a pvalue of 0.4812.
1 - 0.4812 = 0.5188
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 219 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.9. Round answers to 3 decimal places where possible.
A. The sampling distribution follows a _______ distribution.
B. With 90% confidence the population mean number of visits per week is between _____ and ______ visits.
C. If many groups of 220 randomly selected members are studied, then a different confidence interval would be produced from each group. About ________ percent of these confidence intervals will contain the true population mean number of visits per week and about__________ percent will not contain the true population mean number of visits per week.
Answer:
A. Normal
B. Between 2.078 and 2.722 visits.
C. About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.
Step-by-step explanation:
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]
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
Question A:
By the Central Limit Theorem, normal.
Question B:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{2.9}{\sqrt{219}} = 0.322[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.4 - 0.322 = 2.078 visits
The upper end of the interval is the sample mean added to M. So it is 2.4 + 0.322 = 2.722 visits.
Between 2.078 and 2.722 visits.
Question c:
90% confidence level, so 90% will contain the true population mean, 100 - 90 = 10% wont.
About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.
The original price of a book is $25. The book is on sale for 30% off.
What percent of the price are we paying? What is the price you will pay
for the book?
Answer:
You will pay 70% of the original price. You will pay $17.50
Step-by-step explanation:
100% is full price because 100%=1 (one whole).
100% - 30% = 70%
70% = 0.7
0.7 multiplied by $25 is $17.50
Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the Alternate hypothesis
Answer:
Alternative Hypothesis:H₁: μ ≠ 0.41
Step-by-step explanation:
Step(i):-
Given that the newscast reaches 41% of the viewing audience in the area
The mean of the Population = 0.41
Given that In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station
Given that the mean of the sample = 0.36
Step(ii):-
Null hypothesis: The sample statistic does not differ significantly from the hypothetical parameter value.
Given data
Null hypothesis: H₀ : μ = 0.41
Alternative Hypothesis: Any hypothesis which is complementary to the Null hypothesis
Alternative Hypothesis:H₁: μ ≠ 0.41
An angle measures 60.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the angles are 120.1 and 59.9
Step-by-step explanation:
supplementary means that the add up to be 180
I made a system of equations and to make thing faster I graphed them but if you wanted you could solve fully
x+y=180
y-60.2=x
Find the area of this parallelogram, top= 14 left= 11 right = 10
Answer:
140 cm^2
Step-by-step explanation:
Formula for area of a Parallelogram: base*height
14 cm * 10cm = [tex]140 cm^{2}[/tex]
what is the solution to 2(3m+4)=6(1-2m)
a) m=2
b) m=-2
c)m=-10
d.)m=1/5
Answer:
The answer is in the picture below.
Step-by-step explanation:
Simplify 1 1/8 x 4 +2 5/6 x 3
Answer:
bro just search it on mathaway or calculator soup
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
If Jordan rode his bike for five days how much hours dose he ride it for? PLEASE COMMENT YOUR ANSWER asp
Answer: 2880 hours
Explanation: 120 days times 24 hours
Find the amount due if $200 is borrowed for 10 months at an APR of 16% simple interest
Amount =?
Answer
$266.66
Step-by-step explanation:
We have here ,
Principal = $200 Rate = 16% Time = 10 months = 10/12 yrs.We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .
⇒ SI = P × R × T / 100
⇒ SI = $ 200 × 16 × 10 / 12 × 100
⇒ SI = $ 26.66
Now Calculate amount as ,
⇒ A = SI + P
⇒ A = $ 200 + $ 26.66
⇒ A = $ 226.66
Yuhhh please help ty :))
Answer:
20 oz.
Step-by-step explanation:
Hope this helps ! :)
Find the mean of 9, 2, 2, 1, 1 graphically.
Find the average of the function over the given interval. f(x) = x3 over [−1, 1]
9514 1404 393
Answer:
0
Step-by-step explanation:
f(x) = x^3 is an odd function, so is symmetrical about the origin. Its average value on any symmetrical interval around the origin will be 0.
The average value is 0.
Help!!!!!! Which function is best represented by this graph
Answer:j
Step-by-step explanation:
Answer:
J
Step-by-step explanation:
Given: Circle O; ZA intercepts BC; ZD intercepts BC Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Prove: ZA ZD Statements Reasons D 1. given A 1. circle O; ZA intercepts BC, ZD intercepts BC 2. m ZA= (MBC ) 3.m4D = 1mBC) (MBC 12.1? B 3.? 4. mZA=mZD 4. substitution property 5. ZASZD 5. definition of congruent angles O inscribed angles theorem
Answer:
A. Inscribed angle theorem
Step-by-step explanation:
The missing reasons in the proof are inscribed angles theorem.
What is an arc in a circle?In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
Given that, a circle, with arcs AD and BC, we need to find the reason in the proof,
The reasons are inscribed angles theorem.
Inscribed angles theorem :-
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.
Hence the missing reasons in the proof are inscribed angles theorem.
Learn more about arcs, click;
https://brainly.com/question/29886215
#SPJ7
10. Which of these is NOT a perfect square?
a. 81
b. 100
C. X2
d. 42
Answer: 42 is not a square of a whole number
Step-by-step explanation: 81= 9², 100= 10², x²= x·x, 6²= 36 and 7²= 49
Plz I need help with this
Answer:56
Step-by-step explanation:
What is the total surface area of the triangular prism shown?
Answer:
24 2/5ft
Step-by-step explanation:
add all the sides together.
4ft x 2
3ft x 2
10 2/5 x 1
=
24 2/5
How come the tutors don't work??
Answer:
What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer
the Mods are Annoying and very skeptic of the Guidelines of Brainly.
X = {1,3,5,7)
Y = {13,57}
Which of the following is the set XnY?
Answer:x is a letter in music.} 3. Determine whether each set is well-defined. If it is not well-defined, explain why, ... true (e) {1, 3, 5, 7, 9) = {1, 5, 9, 3, 7) false_(f) {1,3,5, 9) = {1,3,5,9} ... Describe each of the following sets as either finite or infinite. ... 13 listened to heavy metal and alternative rock; 12 listened to rap and alternative rock;. or
x 2 - 2yZ = 7 with x = 2v + 1 and y = 2b + 1. These have solutions. (x, y; v, b) = (3, 1; 1,0), (5,3; 2,1), (13,9; 6,4),. (27,19; 13,9), (75,53; 37, 26), (157,111; 78, 55), .
Step-by-step explanation:
what is the domain of this exponential function , y=7^x
Answer: hope this helps
Step-by-step explanation:
Answer:
Hope this helped!!!
Step-by-step explanation:
Emilio’s truck has a gas tank that holds 25 gallons of gas and can travel 400 miles without refilling the gas tank. The graph below shows the amount of gas remaining in Emilio’s truck after he has driven a certain number of miles. Which of the following best describes a reasonable range for this situation
Answer:
[tex]Range: 0 \le y \le 400[/tex]
Step-by-step explanation:
Given
[tex]Gas = 25 gallons[/tex]
[tex]Distance = 400miles[/tex] --- max
Required
The range of the function
The graph is not given; however, the question can be answered without the graph.
From the question, we understand that the truck can hold up to 25 gallons.
This represents the domain (i.e. from 0 to 25)
When the truck is empty (i.e. no gas in it), the truck cannot move any distance (0 miles).
When the truck is filled up (i.e. 25 gallon), the truck can move up to 400 miles.
This represents the range (i.e. from 0 to 400 miles)
Hence, the range is:
[tex]Range: 0 \le y \le 400[/tex]
solve 6×1/5 solve the equation
Step-by-step explanation:
6/5is the answer................
Answer:
1 and 1/5
Step-by-step explanation:
6 times 1/5 is 1/5+1/5+1/5+1/5+1/5+1/5 which equals to 6/5 which also equals to 1 and 1/5
A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 2,200yd2, determine the radius of the region (the radius is length of the stream of water). Round the answer to the nearest yard.
Answer:
Radius = 26 yards.
Step-by-step explanation:
The complete rotation of the sprinkler makes a circle of radius R (R is the length of the stream of water).
Remember that the area of a circle of radius R is:
A = pi*R^2
where pi = 3.14
In this case, we know that the area is equal to 2,200 yd^2
Then:
A = 2,200 yd^2 = 3.14*R^2
Solving this equation we can find the value R.
(2,200 yd^2)/3.14 = R^2
√( (2,200 yd^2)/3.14) = R = 26.47 yards.
We want to round it to the nearest yard, then we need to look at the first digit after the decimal point. It is smaller than 5, then we round down, we get:
Radius = 26 yards.
Please help me! This is due tomorrow and I really need some help! Thank you.
Answer:
over 1/2 own a dog
Step-by-step explanation:
Answer:
Over 1/2 of students own a dog.
Step-by-step explanation:
Total number of students: 25 Add the students owning different types of pets
13/25 Number of students owning dogs divided by total number of students
13/26 = 1/2; therefore 13/25 > 1/2
Need help on this question thanks
Answer:median
Step-by-step explanation: because median is used to be in the middle so those are numbers that would be in the middle, and if you add them up it would contain a high amount of number but if you subtract half you get your answer, and your Welcom!
please help i don't understand this question
A the cost of buying the tablet
B the cost per month of internet service
C the number of months after wich the total cost is 0 dollars
D none of the above
Answer:
Pretty sure it would be b because it keeps scaling as the x axis continues with time
1) Determine the area of the shaded region.
14 ft
8 ft
Answer:
61.73 ft ^2
Step-by-step explanation:
area of rectangle
14x8 = 112
area of circle
π(4)(4) = 50.27
subtract
112-50.27 = 61.73
Substituting the equation x = 4y – 12 into the equation -2y = x – 6 will produce the equation _________.
Round to one billion place. Drop the zeros.
28,436,297,825
30,943,267,101
45,831,246,935
Answer:
28,436,297,825
30,943,267,101
45,000,000,000
Step-by-step explanation:
ur welcome
Find the lengths of the legs.
(NO LINKS)
Given:
The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]
To find:
The lengths of the legs.
Solution:
Two angles are given. By using the angle sum property, the third angle is:
Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]
= [tex]45^\circ[/tex]
Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.
Let x be the lengths of both legs. Then by using Pythagoras theorem, we get
[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]
[tex](10)^2=x^2+x^2[/tex]
[tex]100=2x^2[/tex]
[tex]\dfrac{100}{2}=x^2[/tex]
[tex]50=x^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{50}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
The side length cannot be negative. So, the only value of x is [tex]5\sqrt{2}[/tex].
Therefore, the length of the both legs is [tex]5\sqrt{2}[/tex] units.