Every Thursday, Matt and Dave's Video Venture has “roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a
second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?

I saw other questions for this but why is the standard deviation 0.15*sqrt of 30 and not 0.15*30 because I thought this is a linear transformation

Answers

Answer 1

Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total  amount paid for these second movies will exceed $15.00.

In a normal distribution 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]

It 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, which is the percentile of X.For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard error is [tex]s = \sigma\sqrt{n}[/tex]

In this problem:

Mean of $0.47, standard deviation $0.15, hence [tex]\mu = 0.47, \sigma = 0.15[/tex]30 instances, hence [tex]n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216[/tex]

The probability is 1 subtracted by the p-value of Z when X = 15, hence:

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

Considering the n instances:

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

[tex]Z = \frac{15 - 14.1}{0.8216}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

0.1357 = 13.57% probability that the total  amount paid for these second movies will exceed $15.00.

A similar problem is given at https://brainly.com/question/25769446


Related Questions

Half a number is subtracted from 7 results in 34

Answers

Answer:

[tex]-54[/tex]

Step-by-step explanation:

If the number being halved is x, we can write the expression

[tex]7-0.5x=34[/tex]

Now, bring like terms and solve!

[tex]-0.5x=27[/tex]

Multiple both sides by -2 and you get

[tex]x=-54[/tex]

Wanna check the answer? Well...

[tex]7-(-54*0.5)=7+27=34[/tex]

Translate the phrase into an algebraic expression: 12acorns per qsquirrels?

Answers

Answer:

12/q  acorns/squirrel

Round 512.45 to the nearest ones place.

Answers

512
hope this helps!

The answer would be 512.

From 175 yards away, a marksman hit 14/50 of the targets last year.

Answers

BOOOOGAAAAAAAAAAAAAAAAAAAAA

Consider the following data for 120 mathematics students at a college concerning the languages French, German, and Russian:
65 study French, 45 study German,
42 study Russian , 20 study French and German,
25 study French and Russian,
15 study German and Russian.
8 study all three languages.
Determine how many students study exactly 1 subject and fill the correct numbers of students in each eight region of Venn diagram shown in figure.

Answers

Answer:

check online for more information

The Venn diagram for given situation is as shown below.

The number of students who study exactly one subject = 56

What is set?

"It is a collection of well-defined elements"

What is Venn diagram?

"It is a pictorial representation that uses circles to show the relationships among sets."

For given example,

We have been given the data for 120 mathematics students at a college concerning the languages French, German, and Russian

Let set A, B and C represents the number of students who study French, German and Russian respectively.

⇒ n(A) = 65

⇒ n(B) = 45

⇒ n(C) = 42

20 study French and German

⇒ n(A ∩ B) = 20

25 study French and Russian,

⇒ n (A ∩ C) = 25

15 study German and Russian.

⇒ n(B ∩ C) = 15

8 study all three languages.

⇒ n(A ∩ B ∩ C) = 8

So, the Venn diagram for given situation is shown below.

Now, we find the number of students who study exactly one subject.

28 students study French only, 18 students study German only and 10 students study Russian only.

So, the total number of students who study exactly one subject is,

28 + 18 + 10 = 56

Therefore, 56 students study exactly one subject

Learn more about Venn diagram here:

https://brainly.com/question/1605100

#SPJ2

How do the 2s in 12.5 and 0.912 compare?

A The value of the 2 in 12.5 is 11,000 the value of the 2 in 0.912.

B The value of the 2 in 12.5 is 1100 the value of the 2 in 0.912.

C The value of the 2 in 12.5 is 10 times the value of the 2 in 0.912.

D The value of the 2 in 12.5 is 1,000 times the value of the 2 in 0.912.

Answers

Answer:

  D The value of the 2 in 12.5 is 1,000 times the value of the 2 in 0.912

Step-by-step explanation:

The value of a digit in a number can be found by setting the other digits to zero.

The value of 2 in 12.5 is 2.

The value of 2 in 0.912 is 0.002.

The ratio of values is 2.000/0.002 = 2000/2 = 1000.

The value of 2 in 12.5 is 1000 times the value of 2 in 0.912.

Answer:

D

Step-by-step explanation:

The answer is D

Write an equation and solve the sum of twenty one and five
times a number f is 61

Answers

21 + 5f = 61
5f = 40
f = 8

An account earns simple interest. Find the annual interest rate. I = $60 P = $500 t = 2 years The annual interest rate is %. 10​

Answers

Answer:

100

Step-by-step explanation:

A = P(1 + rt)

A = 500(1 + (0.1 × 2)) = 600

A = $600.00

600-500= 100

please help me please​

Answers

[tex] \frac{76}{90} [/tex]

-_-

The ratio of girls to boys in a bicycling club was 2:3 they were 27 boys how many total members were there in the club

Answers

There were 18 girls because 27 divided by 3 is 9 so then you do 2 times 9 which is 18 :)

Answer:

45

Step-by-step explanation:

Ratio is 2girls:3boys

if there were 27 boys, we would have the following ratio:

2g    xg

--- = ---

3b     27b

To get from 3 to 27, multiply by 9.

Now, do the same for the numerator.

Now we know we have 18 girls!

We can add:

27 boys and 18 girls=

45 members!

a computer performs a calculation in 3.5 x 10^-5 seconds to solve a math problem. How long does the computer need to calculate the solutions to 5 x 10^4 math problems. Enter your answer in standard form

Answers

Step-by-step explanation:

let's do this in 2 steps :

1. go for 1×10⁴ math problems

2. multiply that result by 5 to fully cover 5×10⁴

1.

3.5×10^-5 × 1×10⁴ = 3.5×10^-1

2.

5 × 3.5×10^-1 = 16.5×10^-1 = 1.65×10⁰

so, the computer needs 1.65×10⁰ or simply 1.65 seconds.

Which of the following will have the same value as 350 × 10?

Answers

Answer: 3500x1 or 35x100

Step-by-step explanation:

350x10=3500

3500x1=3500

35x100=3500

Q.

x ÷ 2 = 1.000.000.000
x = ?​

Answers

x÷2=1.000.000.000

x=1.000.000.000×2

x=2.000.000.000

Check:

2.000.000.000÷2=1.000.000.000

♪Answer :

let's find the value of x

x ÷ 2 = 1.000.000.000x = 1.000.000.000*2x = 2.000.000.000

how do I solve it? I don't know how, I can't remember and I don't have my notes ​

Answers

Answer:

-2

Step-by-step explanation:

    [tex]\frac{(-2)^3+3 (4)}{-8+6}[/tex]

 [tex]= \frac{-8 + 12}{-2}[/tex]

 [tex]= \frac{4}{-2}[/tex]    

 [tex]= -2[/tex]

   

Answer:

2.3

Step-by-step explanation:

First we must get rid of the exponent, which is that little 3 at the top.

To do this, we will do:

(-2) × (-2) × (-2) = -8

Now we have -8 + 3.4, which equals -4.6

Next we will combine the numbers in the denominator, to get -2.

Now, all together, we have -4.6/-2.

Last but not least, we will divide -4.6 by -2, to get 2.3

And that's your answer, hope this helps you :)

Sorry if it doesn't, though.

how about these are they correct?​

Answers

Yes, all three are correct

-355 - 165 = - (355+165) = -520

-150 - 126 = - (150+126) = -276

-201 - 124 = - (201+124) = -325

P/s: they are wrong. you need this " () "

ok done. Thank to me :>

22. PLEASE HELP PLEASSSSSSEEEEEEEEEEEEEEE
15 points

Answers

Answer:

Step-by-step explanation:

2

Which numbers are all divisible by 5?
-)))
A)
224, 777, 215, 466, 991
B)
335, 105, 430, 375, 265
©
235, 111, 730, 374, 232
D
332, 350, 265, 425, 510

Answers

Answer: B) 335, 105, 430, 375, 265

Step-by-step explanation:

Since each number ends in either a 5 or a 0, they are all divisible by 5.

Therefore, B is the correct answer.

Answer:

335, 105, 430, 375, 265

335, 105, 430, 375, 265

1. is 2/3 and 4/12 equivalent or no 2. is 5/6 and 10/12 equivalent or no 3. is 1/4 and 4/8 equivalent or no?

Answers

6/12, 1/2, 10/20, 5/10,

Answer:

Step-by-step explanation:

A customer purchased 3 pairs of jeans for $94.50. If each pair of jeans costs the same amount, write an equation and then solve for the amount a single pair of jeans costs

Answers

Answer:

One pair of jeans will cost $31.50

Step-by-step explanation:

To find how much one pair of jeans will cost let's write an equation

where the cost of one pair of jeans is x

∴ 3×x=94.50

to find x we will divide both sides by 3

∴3÷3×x=94.50÷3

which makes the equation

x=31.50

meaning that one pair of jeans costs $31.50

if each pairs of jeans is the same amount

94.50=3*x

solve for x

94.59/3=x

31.50=x
each pair of jeans will cost $31.50

HELP 40 POINTS!!!!!!!!!​

Answers

y - 5 = -1.75(x + 3)
this may be the answer. I’m not completely sure though. X=4y-41/7 or x equals four y minus 41 over 7 :)))

Solve for x + (1/x):

3x + (2/x) - 4 = 2(x+9) - (7 - (1/x))

Answers

Answer:

Step-by-step explanation:

Emma runs 12 miles in 5 hours. How many miles can Emma run per hour?

Answers

Answer:

2.4 miles per hour

Explanation:

Since you ran 12 miles in 5 hours, you have to divide 12 by 5 to get the total amount of miles for 1 hour.

a playground is 750 M long and 250 m broad find the cost of levelling at rupees 16 per 100 square metres​

Answers

Answer:

Area of play ground = Length × Breadth = 750 × 250 = 187500. a Cost of levelling the ground = 187500 × 16 100 = Rs . 30000 

i need help with number 5

Answers

B : 3x-5

You can find this by solving the first equation for y, you do this by adding y and subtracting 5.

Hope this helps!!

A pirate was digging a hole on an island to bury his treasure. If he is able to dig a hole into the sand at 2 feet per minute, what integer would represent how deep the would be after 7 minutes?

Answers

Answer:

2(7) = 14 ft.

Step-by-step explanation:

That pirate must be a beast! or have an excavator.

If
x
=
4
and
y
=
5
, evaluate the following expression:
2
(
y

x
)

Answers

Answer:

2 because if y is 5 and x is 4 and we subtract them and get one and then multiply it by two to get two using pemdas

2(5-4) = 10-8 = 2

The answer is 2

Someone help me it’s number 12
You need to find the x value

Answers

k(x)=34
k(34)=-5(34)+14
-5(34)+14=-156
I think

What is the slope please help you’ll be marked brainliest TYSMMMMMM

Answers

Step-by-step explanation:

the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point to another.

I think I can recognize two good points with integer coordinates :

(-30, -90) and (70, 70)

x changes by +100 (from -30 to 70)

y changes by +160 (from -90 to 70)

the slope is then +160/+100 = 16/10 = 8/5

[tex]\frac{\sqrt{2x} }{\sqrt{} x-1}[/tex]
For which values of x does each expression make sense?

Answers

Answer:

The expression is unclear so:

If the denominator is [tex]\sqrt{x}-1[/tex] then your set of existence is given by

[tex]\left \{ {{x\ge0} \atop {x\ne1}} \right.[/tex]

since you want the quantity inside both square roots to be positive (and it happens for both to be simply [tex]x\ge0[/tex] and you don't want a zero at the denominator so you have to rule out 1.

If the square root includes the whole denominator [tex]\sqrt{x-1}[/tex] the condition becomes [tex]\left \{ {{x\ge0} \atop {x>1}} \right.[/tex]

where you don't include the extreme in the second condition since, again, you don't want to divide by 0. The answer in this case is simply [tex]x>1[/tex] since values between 0 and 1 will give a negative root which is not a real number.

Phil must lay concrete down for his back patio and
purchased 23 cubic feet of concrete, what are possible
dimensions of the patio slab? Select all that apply.

Answers

Answer:

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 6 inches for a patio if the concrete costs $42.00 per cubic yard?

Step-by-step explanation:

I HOPE THIS HELPS

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