Answer:
14
Step-by-step explanation:
A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on 5 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 35.
Required:
What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?
Answer:
0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount
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 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.
A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6.
This means that [tex]\mu = 30, \sigma = 6[/tex]
5 consecutive weekdays.
This means that [tex]n = 5, s = \frac{6}{\sqrt{5}} = 2.6832[/tex]
What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?
This is 1 subtracted by the pvalue of Z when X = 35.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 30}{2.6832}[/tex]
[tex]Z = 1.86[/tex]
[tex]Z = 1.86[/tex] has a pvalue of 0.9686
1 - 0.9686 = 0.0314
0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount
The answer I don’t know math and at this point I’m gonna fail 8th grade this is my last resort pls
Answer:
1: 107°
2: 73°
Line b and a is same. So, straight line is 180°. hence, 180-107=73
For every 2 hours, approximately $1,302 worth of product is sold to consumers. How much money will the company make from selling this product for an entire month (30 days)? what's the answer
Answer:
391,248 dollars
Step-by-step explanation:
A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 42 minutes concentrating on their professor during the hour lecture. The standard deviation was 12 minutes.
Round your answers to two decimal places.
A. The sampling distribution follows a ____ distribution.
B. With 95% confidence the population mean minutes of concentration is between_____ and_____ minutes.
C. If many groups of 150 randomly selected students 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 minutes of concentration and about ______ percent will not contain the true population mean number of minutes of concentration.
Answer:
A. Normal
B. Between 40.08 minutes and 43.92 minutes.
C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
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, a normal distribution.
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 - 0.95}{2} = 0.025[/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 - 0.025 = 0.975[/tex], so Z = 1.96.
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 = 1.96\frac{12}{\sqrt{150}} = 1.92[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes
Between 40.08 minutes and 43.92 minutes.
Question C:
x% confidence interval -> x% will contain the true population mean, (100-x)% wont.
So, 95% confidence interval:
About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
Draw a line tangent to the circle at the point (0, 4). Write an equation for this tangent line. Explain your work.PLEASE HELP
Answer:
y = 1/4x + 4
Step-by-step explanation:
Which of the pairs (2, 3), (1, 2.5), (6, 1), or (−2, 2) is the solution to the equation 4y−x= 10?
Answer:
(2,3)
Step-by-step explanation:
4(3)-(2)=10
12-2=10
The answer is (2,3)
...
6
2.
Find the value of x in the parallelogram below.
33
16
Answer:
sorry where is the parallelogram
Answer:
your question is imcomplete
Step-by-step explanation:
1.The amount of space around an object.
2. The amount of space inside the boundary of a flat object such as a triangle or circle , or surface of a solid object .
3. A measure of how much space it object takes up.
Answer:
MassSurface areaVolumeStep-by-step explanation:
The size of a surface. The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle, or surface of a solid (3-dimensional) object
Mass
A property of a physical body and a measure of its resistance to acceleration when a net force is applied.
Surface
The area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
Volume
The Measure of the amount of space that a substance or an object takes up.
What is the missing number?
Answer:
y = 2^{x}
Step-by-step explanation:
Given the above data for x and y.
From the algebraic expression;
y = 2^{x}
We can deduce that the value of y is equal to two (2) raise to the power of x.
When x = 1, y = 2
y = 2^{x}
y = 2^{1}
y = 2
When x = 2, y = 4
y = 2^{x}
y = 2^{2}
y = 4
When x = 3, y = 8
y = 2^{x}
y = 2^{3}
y = 8
The above calculations can be used to determine the other values of y with respect to x.
Can a right triangle be made from given side lengths 4 in,6 in, 8in
Answer:
no
Step-by-step explanation:
I dont know how to explain but I did the work and it was clearly not a right angle
Which of the following best describes the graph of the logarithmic function
given below?
Answer:
A) Decreasing
Step-by-step explanation:
By graphing the logarithmic equation, we can see that as the x value increases, the y value decreases. Therefore, we say that the graph is decreasing.
Answer:
decreasing
Step-by-step explanation:
Alicia, Jamar, and Tia collect dimes for charity. Alicia collects (3k+4) dimes. Jamar collects twice as many dimes as Alicia. Tia collects 4(5+6k) dimes. How many dimes do they collect altogether in terms of k?
Answer:
33k+32
Step-by-step explanation:
Assign Variables :
Alicia- A
Jamar- J
Tia- T
Write equations :
A = (3k+4)
J= 2(3k+4)
T=4(5+6k)
Simplify equations:
A= 3k+4
J= 6k+8
T= 20+24k
Add:
(3k+4)+(6k+8)+(20+24k)
3k+6k+24k+8+20+4
33k+32
I hope this helps :)
A shirt is on sale for 35% off the original price. If the original price is $39.00 what is the sale price?
Answer:
$25.35
Step-by-step explanation:
You just take off the percentage from the original price to get your final answer.
Hope this helps c:
If f(x)=(x-3)^2+1 what is f(6)
Pls help
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
5m²+15m=0
t²-5t+6=0
5p²+12p+4=0
2a²+10a-48=0
x(2x+5)=0
Answer:
m=1, m= -3
t=3, t=2
p= -0.4, p= -2
a= 3, a= -8
x=0, x= -2.5
Answer:
I hope this helps a little bit.
It Is Not Fake
It Got Answers Promise
Consider the function f(x) = 2 + 2x - 15. What are the x-intercepts of the function?
Answer:
x=6.5
Step-by-step explanation:
I got the x- intercept as 6.5 because I found the x value when y equals 0.
0=2+2x-15
Next, I added 2+-15 and got -13.
0=2x-13
Then, I added 13 to both sides so that I could have x by itself.
13=2x
Next, I divided 2 on both sides so I could find the value of x.
6.5= x
In conclusion, the x- intercept of f(x)=2+2x-15 is 6.5.
please someone help me with this ASAP especially with the workout!!
Suppose an empty flatbed railroad car sits on a track as shown below, with a person pulling on a rope with a force of 310 Newtons in a direction of θ=25∘. Since the railroad car can't move in the direction that the person is pulling, not all of the force he is exerting works to move the car down the track. How much force is the person exerting toward the right (the force that would go towards trying to move the car)? ____Newtons The first person wasn't able to move the railroad car. Suppose a second rope is attached as shown below, and someone pulls on the rope in the direction β=18∘ south of east. If it takes 620 N to get the railroad car moving (even if only slightly), how much force must the second person exert in the given direction to get the railroad car to move? _____ Newtons
Force is a vector quantity, and a force can be resolved into its components to get the effect of the force.
The responses are;
a) The force exerted by the first person towards the right is approximately 280.96 Newtons.b) To move the railroad car, the second person must exert a force of approximately 356.49 Newtons.Reasons:
a) The force with which the person is pulling the railroad car, F = 310 N
The vector force on the rope [tex]\vec {v}_{rope}[/tex] = 310 × cos(25°)·i + 310 × sin(25°)·j
Which gives;
[tex]\vec {v}_{rope}[/tex] = 280.96·i + 131.01·jThe component of the vector acting along the railroad, towards the right is the i component
Therefore, the force the person exerts toward the right while trying to move the car is approximately
280.96 Newtonsb) The direction of the rope of the second person, θ = 18°
The force required to get the railroad car moving = 620 N
The force the second person has to exert to the right is therefore;
F × cos(18°) = 620 - 310 × cos(25°)
Therefore;
[tex]\displaystyle F = \mathbf{\frac{620 - 310 \times cos(25^{\circ})}{ cos(18^{\circ})}} \approx 356.49[/tex]
The force the second person must exert in the given direction, is therefore;
F ≈ 356.49 NewtonsLearn more here:
https://brainly.com/question/24596114
Find the measure of the line segment indicated, assume that lines which appear tangent are tangent. (2 questions) PLS help with these problems ! Pls don't just do it for points
Answer:
1
Step-by-step explanation:
Which is a coefficient matrix for the system of linear equations?
Answer:
D. 1Step-by-step explanation:
[tex]-2\left[\begin{array}{cc}x&-1\\3&5\end{array}\right]+\left[\begin{array}{cc}3&8\\-1&6\end{array}\right] = \left[\begin{array}{cc}x&10\\-7&-4\end{array}\right][/tex] ⇒[tex]\left[\begin{array}{cc}-2x&2\\-6&-10\end{array}\right]+\left[\begin{array}{cc}3&8\\-1&6\end{array}\right] = \left[\begin{array}{cc}x&10\\-7&-4\end{array}\right][/tex] ⇒ [tex]\left[\begin{array}{cc}-2x+3&2+8\\-6-1&-10+6\end{array}\right] = \left[\begin{array}{cc}x&10\\-7&-4\end{array}\right][/tex] ⇒[tex]\left[\begin{array}{cc}-2x+3&10\\-7&-4\end{array}\right] = \left[\begin{array}{cc}x&10\\-7&-4\end{array}\right][/tex] ⇒-2x + 3 = x3x = 3x = 1Correct choice is D
Answer:
d
Step-by-step explanation:
someone help me answer this!!
Answer:
27
Step-by-step explanation:
45 x 45 - 36 x 36 = 729 the square root of 729 is 27
Answer:
a = 27 m is the answer.
Step-by-step explanation:
a = ?
b = 36 m
c = 45 m
According to the Pythagoras theorem,
a² + b² = c²
a² + 36² = 45²
a² + 1296 = 2025
a² = 2025 - 1296
a² = 729
a = 27 m
∴ a = 27 m is the length of the missing leg.
What is the most likely meaning of the word endangered?
influenced
exposed
assisted
threatened
Answer:
exposed is another word for endangered
At a football game, a vender sold a combined total of 108 sodas hot dogs. The number of hot dogs sold was 52 less than the number of sodas sold Find the number of sodas sold and the number of hot dogs sold.
Answer:
28 hotdogs were sold and 80 sodas were sold.
'-''-'--'-'-'--''--'-'--'
PQRS is a quadrilateral.
PST is a straight line.
Find the value of y
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since pqrs is a quadrilateral
Total interior angle = 360 (keep in mind)
>PSR = 360-(65+130+95)
>PSR= 360-290= 70
* PST is a straight line :- >PSR + Y = 180 (sum of angle on a straight line)
:. Y= 180-70= 110.
determine length of RT
Answer:
20
Step-by-step explanation:
please help answer
Find the median of the data set. 1470, 1590, 1420, 1215, 1405, 1370, 1465, 1460, 1230
Answer:
the median is the middle number find the middle number of these and there's your answer
Answer:
1420 is the Median
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
angle klj and angle poq :)
Step-by-step explanation:
a bag contains 6 red marbles 2 blue marbles and 1 green marble. find p(not blue)
Answer:
9?
Step-by-step explanation:
Sorry I don't know I think its 9 though
Which is the correct answer?