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
A consumer group wants to know if an automobile insurance company with thousands of customers has an average insurance payout for all their customers that is greater than $500 per insurance claim. They know that most customers have zero payouts and a few have substantial payouts. The consumer group collects a random sample of 18 customers and computes a mean payout per claim of $579.80 with a standard deviation of $751.30.
Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers?
A. Yes, it is appropriate because the population standard deviation is unknown.
B. Yes, it is appropriate because the sample size is large enough, so the condition that the sampling distribution of the sample mean be approximately normal is satisfied.
C. No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied.
D. No, it is not appropriate because the standard deviation is greater than the mean payout, so the condition that the sampling distribution of the sample mean be approximately normal is not satisfied.
E. No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
Answer:
E. No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
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]
In this question:
Standard deviation larger than the sample mean means that the distribution is skewed.
By the Central Limit Theorem, when the distribution is skewed, normality is assumed for samples sizes of 30 or higher. In this question, the sample is of 18, which is less than 30, so the hypothesis test is not appropriated, and the correct answer is given by option E.
please someone help me with this ASAP especially with the workout!!
Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?
Answer:
[tex] {3}^{81}[/tex] is bigger.
Step-by-step explanation:
[tex] {9}^{27} = ( {3}^{2} )^{27} = {3}^{2 \times 27} = {3}^{54} \\ [/tex]
If we compare the exponents of [tex] {3}^{54}[/tex] and [tex] {3}^{81}[/tex] it can be concluded that:
[tex] {3}^{81}[/tex] > [tex] {3}^{54}[/tex]
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.
Which is the correct answer?
which expression is equivalent to 2x + 3y - x - (8 + 1)
1. 5x + 2y - 7
2. 3 (x + y) - 9
3.6 (x + y) - 7
4. x + 3y - 9
Obtain the general solution:
(x-y)(4x+y)dx + x(5x-y)dy = 0
Answer:
y=2x
y=-x
d=0
Step-by-step explanation:
sorry iam not sure i just tray to help
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
Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.) 13x^2 +1 = -10
Step-by-step explanation:
The given quadratic equation is :
[tex]13x^2 +1 = -10x\\\\or\\\\13x^2+10x+1=0[/tex]
The formula to solve a quadratic equation is :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Put a = 13, b = 10 and c = 1
So,
[tex]x=\dfrac{-10\pm \sqrt{10^2-4(13)(1)} }{2(13)}\\\\x=-0.118, -0.651[/tex]
Hence, this is the required solution.
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
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.
'-''-'--'-'-'--''--'-'--'
Solve for x trignometry
9514 1404 393
Answer:
23.44
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation ...
Tan = Opposite/Adjacent
tan(38°) = x/30
x = 30·tan(38°) ≈ 23.4386
x ≈ 23.44
The lines shown below are parallel. If the green line has a slope of-4, what is
the slope of the red line?
10
A.
B. 4
- 10
-5
5
10
C. -4
O
-5
D.
4
10 -
Th slope of red lines is -4
What is parallel lines?Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
The property of parallel lines states that slope of both lines will b same.
Therefore slope of red lines is -4
To know more about parallel lines refer to:
https://brainly.com/question/5020723
#SPJ2
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.
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 restaurant/bar conducted random sampling of bar purchases. In a sample of 17 restaurant patrons, they found that, when the background music tempo was slow, the mean purchase amount was $30.47 with a standard deviation of $15.10. In a sample of 14 patrons in the same restaurant, they found that, when the background music tempo was fast, the mean purchase amount was $21.62 with a standard deviation of $14.80. The bar would like to know if they can conclude that background music tempo leads to different average purchase amounts at the bar. What test should be used
Answer:
Two sample test of means with unknown variance (standard deviation) but assumed equal
Step-by-step explanation:
For the scenario described above, we apply the two sample test means with unknown variance (standard deviation) but assumed equal test because, the there are two differebt or independent groups, each with its owm subjects or observations. The population variance or standard deviation aren't given. However, the variance are assumed to be equal., since the two groups of sample are chosen from the same population. Therefore, for the scenario described above, the most appropriate test would be a Two sample test of means with unknown variance (standard deviation) but assumed to be equal
...
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:
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:
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.
The product of seven plus two and eight minus two
Answer:
56
Step-by-step explanation:
type in calculator 7*((2+8)-2)
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
1 kilogram is equal to 1,000 grams. How many grams are in 4 kilograms, 35 grams?
Answer:
4035 grams
Step-by-step explanation:
Which choices are solutions to the following equation? Check all that apply.
x^2- 5x = -9/4
A. X = -1
B. X = 0.5
C. X= 4.5
D. x = 2
Answer:
the choices that are solutions are a and d sorry ic im wrong
Answer:
answer is option B) X=0.5
Step-by-step explanation:
happy to help:)
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 :)
17. Multiply 3x3y2 by -6xby7.
O A. 18x15y14
O B.-18x2y3
O C. -18x8yº
O D. -9x15y14
Round the number 8899.50241201 to the nearest whole number.
Answer:
8900
Step-by-step explanation:
pls mark brainliest once other person replies
Answer:
8900 bcoz 8899's nearest whole number is 8900
plz mark me brainliest
Write 0.015 in a standard form
Answer:
the answer is 1.5 x 10-2 that's what I got
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