Answer:
a) 0.2
b) 0.0009
c) 0.0298
d) 0.0465 = 4.65% probability that the sample proportion is less than 0.15.
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]
20% of customers entering her store make a purchase.
This means that [tex]p = 0.2[/tex]
180 people
This means that [tex]n = 180[/tex]
a. What is the mean of the distribution of the sample proportion of customers making a purchase?
By the Central Limit Theorem, [tex]\mu = p = 0.2[/tex].
b) What is the variance of the sample proportion?
The standard deviation is:
[tex]s = \sqrt{\frac{0.2*0.8}{180}} = 0.0298[/tex]
Variance is the square of the standard deviation, so:
[tex]s^2 = (0.0298)^2 = 0.0009[/tex]
c) What is the standard error of the sample proportion?
As found in the previous item, 0.0298.
d) What is the probability that the sample proportion is less than 0.15?
This is the p-value of Z when X = 0.15. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.15 - 0.20}{0.0298}[/tex]
[tex]Z = -1.68[/tex]
[tex]Z = -1.68[/tex] has a p-value of 0.0465.
0.0465 = 4.65% probability that the sample proportion is less than 0.15.
If 5x−1>3x+7, then the value of x will be,
Answer: x>4
solution set : x = {5,6,7,8....}
Step-by-step explanation:
5x-1>3x+7
or, 5x-1+1>3x+7+1
or, 5x>3x+8
or, 5x-3x > 3x+8-3x
or, 2x > 8
or, 2x/2 > 8/2
or, x > 4
Use the function below to find f(3).
f(x) = 3.4^x
Step-by-step explanation:
Hey there!
[tex]f(x) = 3. {4}^{x} [/tex]
Then;
[tex]f(3) = 3. {4}^{3} [/tex]
[tex]f(3) = 192[/tex]
Therefore, f(3) = 192.
Hope it helps!
for the binomial distribution with n=4 and p=0.25
a)find the probability of three success
b)at the most three success
c)two or more failures
Answer:
a.) .0469
b.) .9961
c.) .9492
Rounded these check below for full answers
Step-by-step explanation:
a.)
[tex]{4\choose3}*.25^3*(1-.25)=.046875[/tex]
b.)
Porbability of at most 3 successes is equal to 1-p(4)
p(4)=
[tex]{4\choose4}*.25^4=.003690625[/tex]
1-.003690625=.99609375
c.)
two or more failures is equa lto
p(0)+p(1)+p(2)=
[tex]{4\choose0}*.25^0*(1-.25)^4+{4\choose1}*.25^1(1-.25)^3+{4\choose2}*.25^2*(1-.25)^2=.94921875[/tex]
Thank you guys fir the help
Rotate the given triangle 90°
counter-clockwise about the
origin [ 0 -3 5]
[0 1 2 ]
9514 1404 393
Answer:
[tex]\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right][/tex]
Step-by-step explanation:
The rotation matrix for 90° CCW is ...
[tex]\left[\begin{array}{cc}0&-1\\1&0\end{array}\right][/tex]
Then the rotated coordinates are ...
[tex]\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\cdot\left[\begin{array}{ccc}0&-3&5\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right][/tex]
_____
The transformation of each ordered pair is ...
(x, y) ⇒ (-y, x)
Answer:
Step-by-step explanation:
5/3=12/x what does x equal?
[tex] \frac{5}{3} = \frac{12}{x} \\ = > \frac{5x}{3} = 12 \\ = > 5x = 12 \times 3 \\ = > 5x = 36 \\ = > x = \frac{36}{5} \\ = > x = 7.2[/tex]
This is the answer.
Use the Pythagorean Theorem to find the length of the indicated side of the following right triangle. (NOTE: The square-like symbol indicates a 90-degree angle.)
Pythagorean Theorem: a^2 + b^2 = c^2
a = 5
b = ?
c = [tex]\sqrt{61}[/tex]
5^2 + b^2 = ([tex]\sqrt{61}[/tex])^2
25 + b^2 = 61
b^2 = 36
b = 6
Hope this helps!
First gets most Brainly!
Add and simplify
2x
X +
x + 1
e
3 x
x+1
ox(+3)
X + 1
0
4x +1
X + 1
2
X + 1
Answer:
you did it right D is right answer
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.438.43 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.936.93 and 9.939.93
Answer:
The right solution is "68%".
Step-by-step explanation:
The empirical rule is:
[tex]X\sim N(8.43, 1.5)[/tex]
According to the question,
= [tex]P(6.93< \mu < 9.93)[/tex]
= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]
= [tex]P(z(1)-P(z(-1))[/tex]
= [tex]68[/tex] (%)
Thus the above is the right solution.
Find 0.2B
B=[50 10
25 15]
Multiplying a matrix by a scalar results in every entry in a matrix get multiplied by that scalar, as defined,
[tex]a\begin{bmatrix}b&c\\d&e\\\end{bmatrix}=\begin{bmatrix}ab&ac\\ad&ae\\\end{bmatrix}[/tex]
So in our case, ([tex]0.2=\frac{1}{5}[/tex]
[tex]\frac{1}{5}\begin{bmatrix}50&10\\25&15\\\end{bmatrix}=\begin{bmatrix}\frac{50}{5}&\frac{10}{5}\\\frac{25}{5}&\frac{15}{5}\\\end{bmatrix}=\boxed{\begin{bmatrix}10&2\\5&3\\\end{bmatrix}}[/tex]
Hope this helps :)
first person answers this gets 25 points its khan academy algebra 1
a-7=3(b+2)
1. Simplify/Combine like terms
a-7=3b+6
2. Remove a variable
a-7-a=3b+6-a
7=2b+6
3. Isolate the variable
7-6=2b-6
1=2b
4. Divide
1/2=2b/2
b=1/2
1/2g?
tính công thức Taylo đến x^13
Answer:
أنت مجنون ، هل تعرف ذلك؟
Step-by-step explanation:
بنسلفانيا
Find the mean of the data in the pictograph below.
Answer:
12 sundaes
Step-by-step explanation:
Auto technicians working at a shop in a rural residential area noticed that the depth of tire treads was smaller among cars that have more miles on the odometer.
What are the explanatory variable and response variable for this relationship?
Explanatory variable: type of residential area
Response variable: depth of tire tread
Explanatory variable: depth of tire tread
Response variable: miles on the car odometer
Explanatory variable: miles on the car odometer
Response variable: depth of tire tread
Explanatory variable: type of residential area
Response variable: miles on the car odometer
I think its, (B):
Explanatory variable: depth of tire tread
Response variable: miles on the car odometer
Answer:
Your answer is (C)
Explanatory variable: miles on the car odometer
Response variable: depth of tire tread
ED2021
What is the length of de?
Answer: length of DE = 18
Step-by-step explanation:
Since the angles of these two triangles are the same, we can assume that they are similar triangles. To solve for a missing side of a triangle that is similar, you can set up a proportion:
[tex]\frac{27}{15}=\frac{x}{10}[/tex]
To solve for x (the missing length), you would do:
27 × 10 ÷ 15 = 18
You can set up the proportion in any way between the two triangles as long as the two sides correspond to each other. For example, you could have also used the following proportion to solve for x:
[tex]\frac{x}{27} =\frac{10}{15}[/tex]
When you solve for x using this proportion, you would get the same value for x:
10 × 27 ÷ 15 = 18
A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.
How many times greater is the volume of the swimming pool than the volume of the wading pool?
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS NOT A TEST OR AN ASSESSMENT. PLEASE HELP ME WITH THESE MATH QUESTIONS FOR AN ASSIGNMENT!!! Chapter 10 part 1
1. What is an extraneous solution and what type of functions might they occur in?
2. Given a vertical asymptote and horizontal asymptote, how would you begin to find an expression for a rational function?
Answer:
1.
An extraneous solution is a root of a transformed equation that is not a root of the original equation as it was excluded from the domain of the original equation.
It emerges from the process of solving the problem as a equation.
2.I begin like:
The vertical asymptotes will occur at those values of x for which the denominator is equal to zero:
for example:
x² − 4=0
x²= 4
doing square root on both side
x = ±2
Thus, the graph will have vertical asymptotes at x = 2 and x = −2.
To find the horizontal asymptote, the degree of the numerator is one and the degree of the denominator is two.
Solve x/4 > 2 Question 10 options: x ≥ 8 x < –8 x > 8 x ≤ –8
Answer:
x > 8
Step-by-step explanation:
You can start y multiplying both sides by 4 to cancel out the division by 4:
x/4 > 2
*4 *4
x > 8
Answer:
x > 8
Step-by-step explanation:
x/4 > 2
=> x > 2 × 4
=> x > 8
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
Find the length of BC
Answer:
53.68
Step-by-step explanation:
tan54 = bc/39
bc = 39tan54
Step-by-step explanation:
Hey there!
From the given figure;
Angle CAB = 54°
Side AC = 39
To find: side BC
Taking Angle CAB as reference angle;
Perpendicular (p) = BC = ?
Base (b) = AC = 39
Hypotenuse (h) = AB
Taking the ratio of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan(54) = \frac{bc}{39} [/tex]
Simplify it;
1.376381*39 = BC
Therefore, BC = 53.678.
Hope it helps!
Simplify the algebraic expression by combining like (or similar) terms.
2x−y2+3−3y2+2x+1
Answer:
-4y^2 + 4x +4
Step-by-step explanation:
add -y^2 and -3y^2 = -4y^2
add 2x + 2x = 4x
add 3+1 = 4
and then rearrange
Lainey is looking for a new apartment and her realtor keeps calling her with new listings. The calls only take a few minutes, but a few minutes here and there are really starting to add up. She's having trouble concentrating on her work. What should Lainey do? a) Tell her realtor she can only receive text messages O b) Limit the time spent on each call O c) Turn off her phone until she is on a break O di Call her realtor back when customers won't see her on the phone
a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt
help help......................................................................................
Hey there! Is there more text to this? I would love to help, but there is no question.
A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
Learn more about z-score here:
brainly.com/question/13793746
#SPJ5
Kira, Sam, and Josh sent a total of 85 text messages during the weekend. Sam sent 2 times as many messages as Josh. Kira sent 5 more messages than Josh.
How many messages did they each send?
Answer:
Josh: 20 messages
Kira: 25 messages
Sam: 40 messages
The calculation of the mean of a population and the expected value of the probability mass function of a Random Variable (RV) are quite similar. Consider a probability mass function that contains 4 unique Random Variables: 100, 200, 300, 400. If the expected value of the RV can be calculated by simply taking the average of the RVs, what can be said about the corresponding probabilities of each of the 4 RVs
Answer: Hello the options related to your question is missing attached below are the missing options.
A.) The probabilities of the RVs may be equal
B.) The sum of the probabilities of the RVs exceed 1
C.) This is an impossible occurrence
D.) The probabilities of the RVs must be equal
E.) None of the above
answer:
The probabilities of the RVs may be equal ( A )
Step-by-step explanation:
Given that the value of the population mean and the value of probability mass function of a set of random variables are similar
For the Random Variables : 100,200,300,400
The Probability mass function of RV = ( 100 + 200 + 300 + 400 ) / 4
Hence The probabilities of the RVs may be equal
Suppose that the probability that a person will develop hypertension over a life time is 60%. Of 13 graduating students from the same college are selected at random. find the mean number of the students who develop hypertension over a life time
Answer:
The mean number of the students who develop hypertension over a life time is 7.8.
Step-by-step explanation:
For each person, there are only two possible outcomes, either they will develop hypertension, or they will not. The probability of a person developing hypertension is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
Suppose that the probability that a person will develop hypertension over a life time is 60%.
This means that [tex]p = 0.6[/tex]
13 graduating students from the same college are selected at random.
This means that [tex]n = 13[/tex]
Find the mean number of the students who develop hypertension over a life time
[tex]E(X) = np = 13*0.6 = 7.8[/tex]
The mean number of the students who develop hypertension over a life time is 7.8.
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop. These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop
Answer:
From the data The anxiety levels decreases as a result of the workshop
given that the mean value of the differences = -1.1125
Step-by-step explanation:
Number of randomly selected employees = 16
From the data It can be noticed that the difference in anxiety levels decrease ( Tends towards values below 0 )
To determine this we have to determine the mean value of the differences
(-3) + (-3) + (-2) +(-2) +(-2) + (-2 ) + (-1) + (-1) + (-1) + (-1) + (-1 ) + 0 + 0 + 0 + 0 + 1 / 16
= -18 / 16 = - 1.1125
mean value = -1.1125.
Question 4
A sector of a circle has a diameter of 16 feet and an angle of 2pi 5 this is a fraction by the way) radians. What is the area of the sector?
Answer:
40.2
Step-by-step explanation:
Diameter = 16, Radius = 16/2 = 8
Central angle = 2π/5 radians = 72°
Sector area,
8²π×(72/360)
= 64π/5
= 40.2 (rounded to the nearest tenth)
Answered by GAUTHMATH
