The management of a restaurant has been studying whether or not new customers return within a month. The collected data reveal that 60% of the new customers have returned. If 90 new customers dine at the restaurant this month, what is the probability that at least 60 will return next month? Use Normal approximation to Binomial distribution.

Answers

Answer 1

Using the normal approximation to the binomial, it is found that there is a 0.119 = 11.9% probability that at least 60 will return next month.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].

In this problem, we have that:

60% of the new customers have returned, hence p = 0.6.90 new customers dine at the restaurant this month, hence n = 90.

Thus, the mean and the standard error for the approximation are given as follows:

[tex]\mu = np = 90(0.6) = 54[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{90(0.6)(0.4)} = 4.6476[/tex]

Using continuity correction, the probability that at least 60 will return next month is P(X > 60 - 0.5) = P(X > 59.5), which is 1 subtracted by the p-value of Z when X = 59.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{59.5 - 54}{4.6476}[/tex]

Z = 1.18

Z = 1.18 has a p-value of 0.881.

1 - 0.881 = 0.119.

0.119 = 11.9% probability that at least 60 will return next month.

More can be learned about the normal distribution at https://brainly.com/question/24663213


Related Questions

I’m having trouble can someone find this answer out

Answers

Answer:

f(x) = 13 when x = 10.

Step-by-step explanation:

[tex]f(x)=\frac{x}{2}+8[/tex]

[tex]f(10)=\frac{10}{2}+8[/tex]

[tex]f(10)=5+8[/tex]

[tex]f(10)=13[/tex]

Therefore, f(x) = 13 when x = 10.

Answer:

13

Solution:Plug in the value of x, which is equivalent to 10, instead of x:[tex]f(10)=\displaystyle\frac{10}{2} +8[/tex]f(10)=5+8f(10)=13

Hope it helps.

Do comment if you have any query.

Find the sum of the first 21 terms of the arithmetic progression.
−7, −11, −15, . . .

Answers

We are given with an AP (Arithmetic Progression) with first term being -7, and the common difference being the difference between any succeding term from any term and the term itself, so common difference = -11 - (-7) = -11 + 7 = -4, so now before finding the sum of 21 terms, let's recall that ;

[tex]{\boxed{\bf{S_{n}=\dfrac{n}{2}\{2a+(n-1)d\}}}}[/tex]

Where, d is the common difference, a is the first term, and n is the number of terms and [tex]{\bf S_n}[/tex], being the sum of n terms, so putting all the values in the formula, we will have ;

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}\{2\times -7+(21-1)-4\}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}(-8+20\times -4)}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-8-80)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-88)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=-21\times 44}[/tex]

[tex]{:\implies \quad \boxed{\bf{S_{21}=-924}}}[/tex]

I need help with this please?

Answers

1320

Step-by-step explanation:

the triangle,1/2×15×20×2=300 .rectangle,17×25=425,20×17=340,15×17=255. sum them up 300+255+425+340=1320

What is the median mean mode and range of 1,3,5,8,10?

Answers

Answer:

Below!

Step-by-step explanation:

Given data: 1, 3, 5, 8, 10

Determining the median of the data:

The median is the "middle number" of the data in ascending or descending order. In this case, the data is already in ascending form. Since the number of digits in the data is ODD, we will use to formula (n + 1)/2 (where "n" is the number of digits) to determine the median.

⇒ (n + 1)/2⇒ (5 + 1)/2⇒ (6)/2⇒ 3

Determining the mean of the data:

The mean of the data is the average number of the data (as said above). To determine the average number (mean), we need to sum the digits in the data and divide it by the total digits in the data. In this case, the sum of the digits in the data is 27 and the total digits in the data is 5.

⇒ Mean = (27)/5⇒ Mean = 5.4

Determining the mode of the data:

The mode of the data is the number that has repeated the most.

⇒ "1" has been repeated once⇒ "3" has been repeated once⇒ "5" has been repeated once⇒ "8" has been repeated once⇒ "10" has been repeated once

Since all the digits in the data has repeated once, all the numbers in the data (1, 3, 4, 8, 10) are the mode.

Determining the range of the data:

The range of the data is the difference of the largest and smallest number (As said above).

⇒ Range = Largest number - Smallest number⇒ Range = 10 - 1⇒ Range = 9

Answer:

Median: 5

Mean: 5.4

Mode: 1, 3, 5, 8, 10

Range: 9

Step-by-step explanation:

Median: the middle value.

Mean: the average (found by adding up all of the numbers and dividing them by the number of numbers in the data set).

Mode: the number that is most frequent.

Range: the difference between the biggest and smallest values.

First, make sure your data set is in numerical order: 1, 3, 5, 8, 10

Median: 5

1, 3, 5, 8, 10

Mean: 5.4
1 + 3 + 5 + 8 + 10 = 27

27/5 = 5.4

Mode: 1, 3, 5, 8, 10

1, 3, 5, 8, 10

All of them, as they all appear once.

Range: 9

10 - 1 = 9

Hope this helps!

find the sum of the first 10 terms 125,50,20

Answers

Answer:

208.3

Step-by-step explanation:

Since the numbers are decreasing as multiples, its a geometric progression.

[tex]S_{n}=\frac{a(1-r^{n} )}{1-r} ; r\neq 1 \ and\ r \ is\ less\ than\ 1\\common\ ratio=\frac{20}{50}=\frac{2}{5}\\ S_{10}=\frac{125(1-(2/5)^{10} )}{1-(2/5)} \\=208.3[/tex]

Solve for the unknown side and find perimeter of the figure below note that the figure is not drown to scale.​

Answers

Answer:

[tex]x = 12\ m,\ perimeter = 63\ m[/tex]

Step-by-step explanation:

Step 1:  Determine x

[tex]\frac{15\ m}{10\ m} = \frac{x}{8\ m}[/tex]

[tex](15\ m*8\ m) = (10\ m * x)[/tex]

[tex]120\ m^2 / 10\ m = x * 10\ m / 10\ m[/tex]

[tex]12\ m = x[/tex]

Step 2:  Determine the perimeter of the figure

[tex]18\ m + 15\ m + 10\ m + 8\ m + 12\ m[/tex]

[tex]63\ m[/tex]

Answer:  [tex]x = 12\ m,\ perimeter = 63\ m[/tex]

PLS PLS PLS PLS HELP ME I HAVE BEEN STUCK FOREVER!!!!

The sum of 3 consecutive integers is 96. Find the 3 integers. Show all work and label answer.

Answers

31+32+33 :) steps

add 31+32+33 to get 96
let x be the lowest integer
x + 1 is the second number
x + 2 is the last number

so, the equation would be:
x + x + 1 + x + 2=96

add together the x’s and numbers to get:
3x + 3 = 96

minus 3 from both sides:
3x=93

divide both sides by 3:

x=31


so, the first number is 31, then 32, and 33

hope this helped!!

Below are the score of 30 students in an oral interview. use the information to find the average score.
Score: 1 2 3 4 5
frequency: 7, 7, 7, 12, 3​

Answers

Step-by-step explanation:

the average score would be 3 i think

A woman bought some large frames for ​$18 each and some small frames for ​$8 each at a closeout sale. If she bought 21 frames for ​$​248, find how many of each type she bought.

Answers

Answer:

8 large frames and 13 small frames

Step-by-step explanation:

Given:
$18 each = large frames

$8 each = small frames

To Find:

⇒  Bought 21 frames for ​$​248, find how many of each type she bought

Solve:

1 Large frame costs = 18 $

Therefore, x large frames costs = 18x $

{where x is the number of large frames she bought}

1 Small frame costs = 8 $

Therefore, x Small frames costs = 8y $

{where y is the number of small frames she bought}

By the given condition :

18x + 8y = 248        {equation 1}

x + y = 21                 {equation 2}

Solve these equations simultaneously, from second equation we get :

x = 21- y

18⋅(21−y)+8y= 248

378 - 18y+8y = 248

-10y = -130

y = 13

Put y = 13 in eq x = 21- y

x = 21  - y

x = 21 - 13

x = 8

So the woman bought 8 large frames and 13 small frames.

~lenvy~

Help me please. Again?

Answers

Answer:

See attached image.

Step-by-step explanation:

Helpppppppppppp me out

Answers

Answer:

1.898×[tex]10^{27}[/tex]

2×[tex]10^{27}[/tex]

Step-by-step explanation:

so, there's what's called standard form in maths. this is where you're given a crazy-long chain of digits and are made to shorten that long number. the great thing about this kind of notation is that it makes reading large quantites easier (like super easy)

when dealing with standard form, the unit before the comma must always be from numbers one to nine, always!!!the digits before the comma must never be zero or anything above 9.99999... never!!! after placing your comma all you have to do is count the number of digits (or in this case, zeros) that number of digits after the comma then becomes the power your 10 is being raised to.it is crucial for you to remember that 10, otherwise your number won't be in it's standard form

I hope you'll find this helpful

please correct any and all errors found :)

Find the area of the polygon

Answers

Answer:

40

put some efforts dude...they are so easy

Answer:

40

Step-by-step explanation:

area of a triangle= ½×base× height½×4×6=10since the polygon ha four equal triangles with the same measurement,multiply by four10×4=40ans=40

hope that helps

With a choking victim, the rescuer will provide abdominal thrusts which should be performed
by:
A. None apply
B. Pressing in the person's chest with hard and fast compressions,
C. Making quick inward and upward thrusts to the abdominal cavity with your fist.
D. Lying the person on their back and pushing up into their stomach and rib cage.

Answers

the answer is C never lie the person down and you don’t press on the chest because it’s in the abdomen

PLEASE HELP ME

Directions: Construct a frequency distribution with six intervals for the given data below. Then determine the following: (10 points) a. Range b. Class size c. interval with highest frequency

Number of kilograms of rice consumed by 30 families in a month

60 33 21 57 24 54 52 50 42 60 20 39 23 42 29 46 40 25 38 35 43 35 38 38 28 58 20 ​

Answers

The frequency distribution table shows the distribution of the rice consumed by the families

The range is 40The class width is 7The interval with the highest frequency is 34 - 40

How to construct the frequency table?

From the question, we have the interval to be:

Interval = 6

Start by calculating the range

Range = Highest - Least

This gives

Range = 60 - 20

Range = 40

Calculate the class width

Width = Range/Interval

This gives

Width = 40/6

Width = 7

So, the classes are: 20 - 26, 27 - 33, 34 - 40, 41 - 47, 48 - 54 and 55 - 61

Using the above classes, we have the following frequency distribution table.

Class Frequency

20 - 26 6

27 - 33 3

34 - 40 7

41 - 47 4

48 - 54 3

55 - 61 4

From the above Frequency Distribution Table, the interval with the highest frequency is 34 - 40

Read more about Frequency Distribution Table at:

https://brainly.com/question/1094036

State six ordered pairs for this function
f(x)=.5x+3

Answers

(0,3) - The y-int, after you can just add 5 to the y-coord for each added 1 to the x-coord.

(1,8)

(2,13)

(3,18)

(4,23)

(5,28)

Donte bought a computer that was 20% off the regular price $1,080. If an 8% sales tax was added to the cost of the computer, what was the total price donte paid for

Answers

Answer:

$933.12

Step-by-step explanation:

So 20% of $1,080 is 216.

1080 - 216 is 864

8% of 864 is 69.12

864 + 69.12 would be $933.12

rectangular floor is 8 yd long and 3 yd wide. what is the area in square feet?​

Answers

Answer:

216 square feet

Step-by-step explanation:

First we must convert both dimensions to feet. 1 yd = 3 feet

8 yd = 24 feet and 3 yd = 9 feet

We got the yd by multiplying by 3 to get the number of fett.

Area of a rectangle = base * height

24 feet * 9 feet = 216 square feet

The set of numbers 1, 5, 13, and 24 contains values for m. What values of m makes the equation below true?

6m+12=42

Answers

Answer:

5

Step-by-step explanation:

Solve the equation first for "m"

6m + 12 = 42

6m = 30 (subtract 12)

m = 5 (Divide by 6)

5 is your answer

Hope this help! Please mark me brainliest, it helps!

kirsty and Flo are raising money for charity; Kirsty raises /ive times as much as Fio, Tiesa
amount they raise is £172.50. How much do they each raise?

THANK U

Answers

Answer:

Kirsty raised £143.75 and Flo raised £28.75

Step-by-step explanation:

x = money raised by Flo

5*x = money raised by Kirsty

6*x = money raised together

6x = £172.50

Now divide each side by 6:

x = £172.50:6

x = £28.75 (money raised by Flo)

£172.50-£ 28.75 = £143.75 (money raised by Kirsty)

Kirsty raised £143.75 and Flo raised £28.75

A case of soda has 12 cans. Each can holds 360 milliliters of soda. What is the total
number of liters of soda in the case?

Answers

Answer:

4.32 Liters

Step-by-step explanation:

12*360 mL= 4320 mL

mL to L= mL/1000

4320/1000= 4.32

Find the area
A. 775
B. 625
C. 475

Answers

Answer:

625 in²

Step-by-step explanation:

Area of the figure = Area of the rectangle + Area of the triangle

Finding the base of the triangle

b² = 25² - 15²b² = 625 - 225b² = 400b = 20 in.

Finding Area

A = 25 x 19 + 1/2 x 20 x 15A = 475 + 150A = 625 in²

Mr. Ferarra is planning a field trip to the history museum for all of the students at his middle school. The school's buses can only transport 144 students. Mr. Ferarra needs to rent more buses for the remaining 290 students.

Answers

Answer:

[tex]s - 144 = 290[/tex]

[tex]s = 434[/tex]

Step-by-step explanation:

the keyword is remaining. Meaning the teacher slready has 144 reserved but needs to get 290 spots more.

find the term to term rule for the following sequence 2,6,18, 54, 162

Answers

*3 or multiply by 3

:)

Answer:

multiply 3 or *3 that is 2*3=6

Does 0 ÷ a =a ÷ a(assume a is not equal to 0)? explain

Answers

Answer:

A = 0

__________________________________________________________

Solve

Although the question says not to assume A is 0, that is the only possible option, since any nor prime or composite is going to be the higher number, because it stays the same.

0 ÷ a(0) = 0

a(0) ÷ a(0) = 0

__________________________________________________________

Questions?

Ask in the comments.

For which inequality is x = 5 a solution

Answers

Answer:

4<x<6

Step-by-step explanation:

4 is smaller than x

and x is samller than 6

so its 5

find a quadratic polynomial each with the given number as the sum and product of its zeros respectively
1/4 and 1​

Answers

Answer:

The answer is 4x² – x – 4 = 0

Step-by-step explanation:

1st Method Given;Sum of zeroes = α + β = (-b)/a = 1/4Product of zeros = αβ = c/a = 1

Where,

a = 4b = 1c = 4

So, one quadratic polynomial satisfying is given condition is 4x² x 4 = 0

2nd Method

Sum of zeroes = 1/4

Product of zeros = 1

Remember this formula

(α + β)x + αβ

x² – 1/4x + 1

4 x 4 = 0

Thus, The quadratic polynomial is

4x² – x – 4 = 0.

Find the volume it’s homework I need help with

Answers

The answer is 1. 4x4x3 = 48 the whole volume 2. 48-4x2= 40.

help i dont know how to do this and i forgot the study guide

Answers

B is the right answer

I hope it will help you

A credit card had an APR of 25.67% all of last year and compounded interest daily. What was the credit card's effective interest rate last year?

a
28.25%
b
29.25%
c
28.92%
d
27.32%

Answers

Answer:

The answer is 29.25%.

Step-by-step explanation:

I think it is B
Hope this is right!!!

The radius of the circle with a central angle of 138° that intercepts an arc with length 9 miles is miles?

Answers

Step-by-step explanation:

\begin{gathered}x^2 + y^2 + 17 = 138\\x^2 + y^2 = 138 - 17\\x^2 + y^2 = 121\\x^2 + y^2 = 11^2\\Radius = 11\end{gathered}

x

2

+y

2

+17=138

x

2

+y

2

=138−17

x

2

+y

2

=121

x

2

+y

2

=11

2

Radius=11

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