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?

Answers

Answer 1

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


Related Questions

Dave's Candy Store is having a 15% off sale on gourmet candy. Jamal paid $37.40 for a gourmet candy basket that was on sale. What was the original price of the candy basket?

Answers

Answer: $43.01

Why: 37.40 x 0.15
= 5.61
(So the discount was $5.61)

Add it back into the sale...
$43.01

The original price of the gourmet candy is $44, as per linear equation.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."

Given, the percent of discount at Dave's candy store is 15% = 0.15.

Sale price of a gourmet candy is $37.40.

Let, the original price of the gourmet candy is x.

Therefore, [x - (x × 0.15)] = 37.40

⇒ (x - 0.15x) = 37.40

⇒ 0.85x = 37.40

⇒ x = (37.40/0.85)

⇒ x = 44

Therefore, the original price of the gourmet candy is $44.

Learn more about a linear equation here: brainly.com/question/2984088

#SPJ2

A lumberyard charges $ 1 per cut to trim boards. Bob buys a 12-ft board and wants it out into twelve 1-ft pieces. How much will he be charged for the cutting? The correct answer is $11.

Answers

Answer:11

Step-by-step explanation:

There are 11 cuts to make 12 pieces on 1ft each

A company manufacturing a roadside lighting system wants to estimate the average illuminance (brightness) at sunset. The illuminance at sunset for the past 10 days was as follows: 406, 385, 389, 383, 352, 379, 388, 343, 368, 387 lux. Construct a 95% confidence intervals for the average illuminance at sunset. Assume that the illuminance at sunset is approximately normally distributed.

Answers

Answer:

(364.595 ; 391.405)

Step-by-step explanation:

Given the sample data:

406, 385, 389, 383, 352, 379, 388, 343, 368, 387

Using calculator :

Sample mean, xbar = 378

Standard deviation, s = 18.74

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/√n

TCritical at df = 24 ; 0.05 = 2.262

Margin of Error = 2.262 * 18.74/√10 = 13.405

Lower boundary = (378 - 13.405) = 364.595

Upper boundary = (378 + 13.405) = 391.405

(364.595 ; 391.405)

5647+34566= please hurry and answer don't put the answer in a link

Answers

Answer:

40213........................

Answer:

5647+34566=40213 is your answer

1. I need some help
2. Answer question step by step
3. Dont Troll or you will be reported​

Answers

Answer:

The shapes are triangles with same base and height

The area of a triangle is the half of the product of the base and height

A = 1/2bh is same for both shapes, so they have same area

Pleaseeeee help!!! I’ll give you best answer!!!!
Solve the equation with the quadratic formula *
10) 3x² =-10x – 5
1-5+2V10 -5 - 2V10
A)
3
3
-5+ V10 -5 - V10
B)
3
3
25
C) -4
4
15+ V10 5 - V10
D)
33

Answers

Answer:

B) x = (-5 + √10)/3 and (-5 - √10)/3 is the answer.

Step-by-step explanation:

3x² + 10x + 5 = 0

a = 3

b = 10

c = 5

Finding the Discriminant (D),

D = b² - 4ac

D = 10² - 4 × 3 × 5

D = 100 - 60

D = 40

√D = 2√10

Using quadratic formula,

x = (-b ± √D)/2a

x = (-b + √D)/2a

x = (-10 + 2√10)/2 × 3

Taking out the common factor 2,

x = (-5 + √10)/3

Similarly,

x = (-b - √D)/2a

x = (-10 - 2√10)/2 × 3

x = (-5 - √10)/3

Answer:

[tex]\huge \red {\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}[/tex]

Step-by-step explanation:

[tex]3 {x}^{2} = - 10x - 5 \\ 3 {x}^{2} + 10x + 5 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 3 \: \: b = 10 \: \: c = 5 \\ now \: by \: quadratic \: formula \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ plug \: a = 3 \: \: b = 10 \: \: c = 5 \: in \: the \\ above \: formula \\ x = \frac{ - 10 \pm \sqrt{ {(10)}^{2} - 4(3)(5) }}{2 \times 3} \\ x = \frac{ - 10 \pm \sqrt{ {100} - 60}}{6} \\ x = \frac{ - 10 \pm \sqrt{40}}{6} \\ x = \frac{ - 10 \pm2 \sqrt{10}}{6} \\ x = \frac{ 2(- 5 \pm \sqrt{10})}{6} \\ x = \frac{ - 5 \pm \sqrt{10}}{3} \\ x = \purple{ \bold{\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}}[/tex]

1,000 meters is the same as 1

Answers

It is equal to 1 kilometer

Please mark brainliest

Somebody please help me. This is geometry. The goal is to find the missing side with A similarity statement. But the more I try on this, it becomes more confusing. Please help. Thx.

Answers

Answer:

50

Step-by-step explanation:

Given:

qrst ~ nkpm

The ratio of corresponding sides (consider the order of letters in the name of figures):

rs/ kp = qt / nmrs / 35 = 60 / 42rs = 35*60/42rs = 50

Answer:

Solution given:

qrst~nkpm

since the side of similar quadrilateral are proportional so

qt/mn=rs/kp

60/42=?/35

?=60/42×35=50

missing side =50 is your answer

Martin can travel 174 miles in 3 hours. At this rate, how far can he travel in 7 hours?

325 miles


398 miles


400 miles


406 miles

Answers

Answer: 406 miles

Step-by-step explanation: First you have to figure out how many miles he traveles per hour and to do that you divide 174 by 3 to get 58. Then multiply that by 7 because that is the amount of hours he should be traveling to get 406

Answer:

406 miles

Step-by-step explanation:

First find how far Martin can travel in 1 hour, then multiply by 7(hours):

174 ÷ 3 = 58

58 × 7 = 406

Giving Brainlest !!!!! If your bank offered you 3% interest on $5,000 in your savings account , how much money would you have in your account at the end of the year after interest ?

Answers

Answer: $5,150

Step-by-step explanation:

5000x0.03=150+5000=5,150

Question 18 (5 points)
If two lines are perpendicular to the same line, then they are
to each other.
A) congruent
B) perpendicular
C) parallel
D) complementary

Answers

two lines are perpendicular to the same line so they are parallel .

4 more than 5 times a number

Answers

Answer:

5x + 4

Step-by-step explanation:

4 more = +4

5 times a number = 5x

Violet is making pizzas for a pizza party. Each pizza requires 5/16 pound of cheese. How many pounds of cheese does she need to make 11 pizzas? Express your answer in simplest form.

Answers

Answer 3 7/16 pounds

Explanation 5/16 times 11/1 =55/16
55 divided by 16= 3 7/16

Amy and Sara's ages are consecutive even integers. The product of their ages is 528. If Sara is
younger, how old is Amy?
Write an equation that can be used to find their ages.

Answers

Answer:

24

Step-by-step explanation:

Sara = x age

Amy = x+2        when Sara  x = 22    Amy is x + 2 = 24

Product of ages = 528 so............

    x(x+2) = 528

    x² + 2x - 528 = 0     solve for x         I did it graphically first to get x = -24, 22

    (x+24) (x-22)  = 0

   (x+24) = 0         (x-22) = 0

           x = -24             x = 22        since you really can't have a negative age

                         

Which of the following is equal to / 9.4

Answers

Answer:

A

Explanation:

both of the will be equaled to sq36

Directions: Evaluate the following combinations and determine the value of the
unknown. Write the complete solutions in your answer sheet.
1. nCs = 126
2. 10Cr= 252
3. C(n, 5) + 8 = 9
4. C(n+1, 7) = 01
5. C(6r, 6-1) = 12 + C(4,2)




what is the answer with solution po​

Answers

Answer:

1. C(9,4) : n=9, s=4

2. C(10,5) : r=5

3. C(5,5) : n=5

4. C(7,7) : n=6

5. C(18,17) : r=3

Step-by-step explanation:

Please help!!! ABCD is a square with diagonals intersecting at E. What is the length of BE

Answers

Answer:

[tex]BE = 4\sqrt2[/tex]

Step-by-step explanation:

Given

The attached square

Required

Find BE

First, we calculate BD (the diagonal) using Pythagoras theorem.

[tex]BD^2 = BA^2 + AD^2[/tex]

Since the shape is a square, then

[tex]BA = AD = 8[/tex]

So:

[tex]BD^2 = 8^2 + 8^2[/tex]

[tex]BD^2 = 2(8^2)[/tex]

Take square roots

[tex]BD = \sqrt{2(8^2)[/tex]

[tex]BD = \sqrt{2} * 8[/tex]

[tex]BD = 8\sqrt{2}[/tex]

BE is half BD.

So:

[tex]BE = \frac{1}{2} * BD[/tex]

[tex]BE = \frac{1}{2} * 8\sqrt2[/tex]

[tex]BE = 4\sqrt2[/tex]

A gym offers classes for students to attend. If both the range and median number of students attending each class was 13 students, which of the following box-and-whisker plots could represent the number of students attending the classes?

Answers

Answer:

3

one

will represent

the student

PLEASE HELP ASAP ???

Answers

Answer:

-1

Step-by-step explanation:

In a swimming competition, Peter swam 600m and Gabriel swam 2km .What is the ratio of Peter’s distance to Gabriel’s? Give your answer in its simplest form.

b. Express the ratio 20cm to 15m in the form 1: n

c. Express the ratio 60 cm to 20 m in the form 1 : n

Answers

Answer:

Yes, because Gabriel is the swimming. He was in 2nd or maybe 10th.

Answer:

Step-by-step explanation:

If cos theta =12/13.find 1+cot theta

Answers

Answer:

17/5

Step-by-step explanation:

If cosθ = 12/13, find (1+cotθ)

As shown in the diagram attached,

Cotθ = 1/tanθ = adjacent/opposite

From the diagram attached,

cotθ = 12/a................... Equation 1

But we can find the value of a by using  pythagoras theorem

13² = 12²+a²

169 = 144+a²

a² = 169-144

a² = 25

a = √25

a = 5.

Substitute the value of a into equation 1

Therefore,

cotθ = 12/5

(1+cotθ) =(12/5)+1 = (5+12)/5

(1+cotθ) = 17/5

The researchers chilled the beverages to 6°C. Participants drank the beverages at the same time each day for three days. During the 3 days of the experiment, the researchers feed each participant the same diet. On the third day participants spent 24 hours in a calorimeter chamber to measure their energy metabolism. The medical journal Obesity published the results in 2007. What is the purpose of double-blinding?

a. To control unintentional researcher bias in the execution of the experiment
b. To control for the participants' prior beliefs about energy drinks
c. To control both unintentional research bias and participant prior beliefs

Answers

Answer:

C. To control both unintentional research bias and participant prior beliefs

Step-by-step explanation:

Double blinding is a type of study where neither the participants nor the researchers know the treatment or intervention that the participants receive until the whole study/research is completed. This is very important because it means that the results gotten from the study have a very slim chance of being biased.

Thus,the correct answer is option C as it includes both the researcher and the participants

Liz has 4 times as many points as Joey in a video game. Together they have fewer than 150 points. Which inequality can be used to determine the least number of points that Joey can have?

A. 4x+4<150
B. 4x+4≤ 100
C. 4x+x<150
D.4x+x≥150
I will select u as brilliant :)​

Answers

Answer:

C. 4x + x < 150

Step-by-step explanation:

x = Joey's points

4x = Liz's Points

together they have fewer than 150 points means the inequality is < 150

So the answer is:  4x + x < 150

Answer:

This may help you I think so

6:45 + 85


No links pls

Answers

so first you wanna break down the 85 minutes so 1 hour is 60 minues now its 7:45 but we still have 25 minutes left sow now we add the minutes it will be 8:05

8:05 is the answer

Answer:

Step-by-step explanation:

The deer population at the local reserve grows exponentially. The current population is 125 deer and the relative growth rate is 16% per year. Find the number of years required for the deer population to be 400.

Answers

Answer:

About 7.84 years before the deer population is 400

Step-by-step explanation:

So first we write our equation

125(1.16)^x = 400

Then we divide all sides by 125

1.16^x=3.2

x log 1.16 = log 3.2

06445798922x=0.50514997832

x= 7.83688700862

7.83688700862 years to go!

Beth wants to buy Christmas lights to decorate her new home. At various stores, Beth found lights priced from $6.99 a strand to $25.99 a strand. Beth bought almost $200 worth of the cheapest lights so that she could have as many lights on her house as possible. For Beth, Christmas lights are a(n) _____.

Answers

Answer:

Christmas lights are price based shopping products

Step-by-step explanation:

From the question we understand that, Beth bought as many cheapest lights as possible. This means that she places value over quantity than quality.

The above is an illustration of price based shopping products where customers (in this case, Beth) see all products (in this case, Christmas lights) as similar products, irrespective of their different qualities (after all, they all light Christmas trees).

Because of this, the customer will opt for least expensive items, leaving the more expensive items.

Verify the identity.
Please show your work.

Answers

Step-by-step explanation:

To prove :

( 1 - sin x ) ( 1 + sin x ) = sec² x

LHS : -

( 1 - sin x ) ( 1 + sin x )

Formula / Identity : -

( a - b ) ( a + b ) = a² - b²

Here,

a = 1

b = sin x

( 1 - sin x ) ( 1 + sin x )

= 1 - sin² x

Identify : -

sin² θ + cos² θ = 1

cos² θ = 1 - sin² θ

Similarly,

1 - sin² x

= cos² x

= RHS

Hence verified.

at a high school, there are 3,510 students. the ratio of seniors to juniors to sophomores to freshmen is 4:6:5:3. How many students are in each class

Answers

Answer:

seniors: 780

juniors: 1170

sophomores: 975

freshmen: 585

Step-by-step explanation:

4 + 6 + 5 + 3 = 18

3510/18 = 195

195(4) = 780

195(6) = 1170

195(5) = 975

195(3) = 585

HELP MEEEE PLEASEEEEEE

Answers

Answer:

The area of the circle is 27

Step-by-step explanation:

Using the formula given to us, we know that the area of the circle = pi times the radius squared. This gives us an indication of what we need to do. We must first understand that the radius of the circle is 3. Multiply the radius by the 2nd power (multiply 3 by 3), and we get 9. They then ask us to substitute 3 for pi, meaning instead of pi times 9, it's 3 times nine, and 3*9=27. And there is your answer.

Plss help mark brain list a lot of point

Answers

Answer:

arc TQ= 69°          (44 + 25)

arc QR = 155°       (180 - 25)

arc TS = 111°         (360 - 44 - 25 - 155 - 25)

arc SQR = 335°    (360 - 25)

arc RQT = 224°    (155 + 25 + 44)

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