Sofia's audio player has 15,000 songs. the play time for the songs is skewed to the right, with a mean of 255 seconds and a standard deviation of 30 seconds. part a: can you accurately calculate the probability that the mean play time is more than 260 seconds for an srs of 15 songs? explain. (4 points) part b: if you take a random sample of 40 songs instead of 15, explain how the central limit theorem allows you to find the probability that the mean play time is more than 260 seconds. calculate this probability and show your work. (6 points)

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that:

a) Since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.

b) There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.

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.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal and the sample size is at least 30.

The mean and the standard deviation are given by, respectively:

[tex]\mu = 255, \sigma = 30[/tex]

In item a, according to the Central Limit Theorem, since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.

For item b, we have that n = 40 > 15, hence the standard error is given by:

[tex]s = \frac{30}{\sqrt{40}} = 4.74[/tex]

The probability is one subtracted by the p-value of Z when X = 260, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{260 - 255}{4.74}[/tex]

Z = 1.05

Z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.

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Related Questions

A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.​

Answers

Answer:

200 KM/H

Step-by-step explanation:

A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.

let x=speed of wind

(840+x)=speed of plane with wind

(840-x)=speed of plane against wind

Travel time = distance/speed (same with and against the wind)

3120/(840+x)=1920/(840-x)

cross-multiply

3120*840-3120x=1920*840+1920x

3120*840-1920*840=1920x+3120x

5040x=1008000

x=200 km/hr

answer

Speed of wind=200 km/hr

Write an equation for each translation y=sin x, pi/4 units to the right

Answers

The equation of the translation is y = sin(x - π/4)

How to determine the translation?

The equation is given as:

y = sin(x)

The rule of translation to the right is:

(x,y) => (x - h,y)

This gives

(x,y) => (x - π/4,y)

So, we have:

y = sin(x - π/4)

Hence, the equation of the translation is y = sin(x - π/4)

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It's always a good idea to check your solutions to any equation in the original equation. When solving an absolute value equation, when must you check for extraneous solutions?

A. Sometimes, when u only get one solution
B. Never
C. Always
D. Sometimes, when the variable appears both inside and outside the absolute value expression

Answers

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression

What is an extraneous solution?

An extraneous solution is a solution that in obtained after completely solving an equation but it does not  work in the original given equation.

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression (Option D).

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Find the measure of side b

Answers

Cos(A) = b/c
b = cos(A)/c
b = cos(40)/270
b =206.8

Answer:

230??

Step-by-step explanation:

If C =270°

And b=40°

270-40= 230

Actually belive the one on top

If y varies directly as x and y = 8 when x = 4, what is the value of y when x = 16? a. 32 b. 16 c. 64 d. 28

Answers

By finding the proportional relation between x and y, we will see that when x = 16, we have y = 32.

How to get the value of y when x = 16?

If y varies directly with x, then we can write the relation as:

y = k*x

Where k is the constant of proportionality.

First, we know that when x = 4, we have y = 8, replacing that we get:

8 = k*4

Solving for k, we get:

k = 8/4 = 2.

Then the relation between x and y is:

y = 2*x

When x = 16, we have:

y = 2*16 = 32

Then the correct option is a.

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What is the perimeter of triangle JKL (same triangle as question #1)?

Answers

Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

Which of the following is the equation of the quadratic function below?
10
-10
10
O A. y = x² +9x-18
OB. y=x²-2x+1
C. y=x²-9x+18
OD. y=x²+2x-1
-10

Answers

Answer:

ehhhh probably C cuz it makes more sense

Find the solution to each system please show your work!

Answers

Answer:

infinite number of solutions

Step-by-step explanation:

x + y = 1 → (1)

3y = - 3x + 3 ( add 3x to both sides )

3x + 3y = 3 ( divide through by 3 )

x + y = 1 → (2)

since the 2 equations are the same, this indicates the system has an infinite number of solutions

What is value of x in the equation 6x+7-2x=3+5x-9

Answers

Answer: x = 13

Step-by-step explanation: First, we simplify the equation to get 4x + 7 = 5x - 6. Then, from there, we subtract 7 on both sides to get 4x = 5x - 13. Then we subtract 5x from both sides, which would give us -x = -13. Finally, we can divide both sides by -1 (because remember, x = 1) to get that x = 13. Hope this helps!

Solve for x. Calculate the area

Answers

Answer:

32 sq inches

Step-by-step explanation:

Hope that given shape is a rectangle.Measures of the opposite sides of a rectangle are equal-> x/2 = 8->x = 8*2-> x = 16 inches-> x/4 = 16/4 = 4 inchesA (rectangle) = 8*4 = 32 sq inches

PLease HELP!!! 20 POINTS!!! WILL GIVE BRAINLIEST!!!

Answers

there is no question though ?

Ok help me I don’t understand stand this

Answers

Answer:

Step-by-step explanation:

Comment

It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.

The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.

Answer

product

12

B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam?
A.4 h
B.6 h 40 min
C.6 h 20 min
D.3h 40 min ​

Answers

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

How long does it take to fill the dam?

Given that;

Amount of water needed to fill the dam A = 30000 litresPump rate r = 75 litres per minuteTime needed to fill the dam T = ?

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

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5. If the longer side of the rectangle is 25.5 in., what are its width, perimeter, and area?

Answers

Step-by-step explanation:

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in

A bank converts U.S. dollars to European euros at a rate of $1 for 0.88 euros. Kelsey wants 100 euros for her trip to Europe.

How much money, in dollars, does Kelsey need to give the bank

Answers

Answer:

$113.64

Step-by-step explanation:

0.88 x $113.636364 = 100 euros

= $113.64

(Hope this helps ^-^)

Find the 5th term of the sequence which has a first term of 1 and has a common ratio of 2.3. Round your answer to the nearest hundredth if necessary.

Answers

The 5th term of the sequence is 27.98

How to determine the 5th term?

The given parameters are:

First term, a = 1Common ratio, r = 2.3

The nth term of a geometric sequence is calculated using:

[tex]T_n = ar^{n-1[/tex]

So, we have:

[tex]T_5 = 1 * 2.3^{5-1[/tex]

Evaluate the difference

[tex]T_5 = 1 * 2.3^4[/tex]

Evaluate the product

[tex]T_5 = 27.98[/tex]

Hence, the 5th term of the sequence is 27.98

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NEED ASAP
What is the rule for the function that is graphed?

Answers

Answer:

C

Step-by-step explanation:

The y-intercept if the graph is 2 and the slope is 2 so the rule is y=2x+2

3(2x-9) - 4(3x + 4) = 2(x − 12) + 7/3
pls answer the question​

Answers

Answer:

[tex]\normalsize \textsf{$x = -\dfrac{8}{3}$}[/tex]

Step-by-step explanation:


Given: [tex]\normalsize \textsf{$3(2x - 9) - 4(3x + 4) = 2(x - 12) + \dfrac{7}{3}$}[/tex]

1. Distribute

For 3:

[tex]\normalsize \textsf{$3(2x - 9)$}\\\normalsize \textsf{$3(2x) + 3(- 9)$}\\\normalsize \boxed{\textsf{$6x -27$}}\\[/tex]

For -4:

[tex]\normalsize \textsf{$-4(3x + 4)$}\\\normalsize \textsf{$-4(3x) + -4(4)$}\\\normalsize \boxed{\textsf{$-12x -16$}}\\[/tex]

For 2:

[tex]\normalsize \textsf{$2(x - 12)$}\\\normalsize \textsf{$2(x) + 2(-12)$}\\\normalsize \boxed{\textsf{$2x -24$}}\\[/tex]

Now we have: [tex]\normalsize \textsf{$6x - 27 - 12x -16 = 2x-24 + \dfrac{7}{3}$}[/tex]

2. Combine like terms:

[tex]\normalsize \textsf{$-6x -43 = 2x -\dfrac{72}{3} + \dfrac{7}{3}$}\\\\\normalsize \textsf{$-6x -43 = 2x -\dfrac{65}{3}$}\\\\[/tex]

3. Subtract 2x from both sides:

[tex]\normalsize \textsf{$-6x-2x -43 = 2x -2x -\dfrac{65}{3}$}\\\\\normalsize \textsf{$-8x -43 = -\dfrac{65}{3}$}\\\\[/tex]

4. Add 43 to both sides:

[tex]\normalsize \textsf{$-8x -43 +43 = -\dfrac{65}{3} + 43$}\\\\\normalsize \textsf{$-8x = -\dfrac{65}{3} + \dfrac{129}{3}$}\\\\\normalsize \textsf{$-8x = \dfrac{64}{3}$}[/tex]

5. Divide both sides by -8

[tex]\normalsize \textsf{$-8x = \dfrac{64}{3}$}\\\\\normalsize \textsf{$-8x \div 8 = \dfrac{64}{3} \div -\dfrac{8}{1}$}\\\\\normalsize \boxed{\textsf{$x = -\dfrac{8}{3}$}}[/tex]

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Karen purchased a used vehicle that depreciates under a straight line method the initial value if the car is 4400 and the salvage value is 800 if the car is expected to have a useful life of another six years how much will it depreciate each year?

Answers

Answer:

Karen expects the vehicle to depreciate by 600 each year.

Step-by-step explanation:

Given:

- initial value: 4400

- salvage value: 800

- another six years

It is expected to depreciate from 4400 to 800 in 6 years.

The depreciation per year is the ratio

depreciation per year = (total depreciation) / (number of years)

Total depreciation is the change in value, so the depreciation per year is

 (4400 - 800)/6 = 600

Solve 7p+ 13 = 30 Give your answer as a fraction in its simplest form.​

Answers

Answer:  p = 2 3/7

Step-by-step explanation:

7p+13 = 30

7p = 17

p = 17/7

p = 2 3/7

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The value of p as a fraction in its simplest form is 17/7

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example:

1/2, 1/3 is a fraction.

2/4 is a fraction but we can simplify further since there is a common factor of 2 with 2 and 4.

2/4 = 1/2 is a fraction.

4/16 = 4/(4x4) = 1/4 is a fraction.

We have,

7p + 13 = 30

Solve for p.

Subtract 13 on both sides.

7p + 13 - 13 = 30 -13

7p = 17

Divide both sides by 7.

p = 17/7

We can not further simplify the fraction as there are no common factors between 17 and 7.

Thus,

The value of p as a fraction in its simplest form is 17/7

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An amusement park charges $5 as an admittance fee and $1.50 per ride. Jason has $20 to spend, but used $3 to buy a
drink and hot dog.
A. Write an inequality that represents the situation,
B. What is the maximum number of rides Jason can go on.

Answers

Answer:

a=

b=8

Step-by-step explanation:

20-5=15 (admittance fee)

15-3=12 (food and drink)

12÷1.5=8 rides because 1.50 is price for every ride

Find the inequality represented in the graph.

Answers

Answer: y > -1/2x + 2

Step-by-step explanation: first, in order to find the inequalities you should find the gradient by choosing two points from the line and you should you the formula m=y2-y1/x2-x1 to find the gradient.

Next, you should find the y-intercept in order to complete the inequality it can be easily found as the y-intercept is the place where the line crosses the y axis

Then you create your equation { y = -1/2x + 2 } and then if above the line is shaded then it is {> greater than} and if below the line is shaded then it should be {< less than}

(so you should replace the equation with the lesser or greater sign according to the way the graph is shaded)

COSINE LAW: Solve triangle PQR. round angles to the nearest tenth​

Answers

Answer:

Hi,

Step-by-step explanation:

PR²=PQ²+QR²-2*PQ*QR*cos(51°)

=15²+12²-2*15*12*cos(51°)

=142,444659....

PR=11.9350...

PQ²=QR²+PR²-2*QR*PR*cos(R)

cos(R)=(12²+142.444...-15²)/(2*12*11.9350...)=0,21451112....

angle R=77,61315...°≈77.6°

angle P=180°-51°-77.6°≈51,4°

Without simplifying, find:
a) the 6th term of (2x+5)^15
b) the 4th term of (x^2+5/x)^9

Answers

Answer:

Part A)

[tex]\displaystyle z_6 = 9609600000x^{10}[/tex]

Part B)

[tex]z_4 = 10500 x^9[/tex]

Step-by-step explanation:

Recall the binomial expansion theorem:

[tex]\displaystyle (x+y)^n = \sum_{k=0}^{n}{n \choose k} x^{n-k} y^k[/tex]

Part A)

Our expression is equivalent to:


[tex]\displaystyle (2x+5)^{15} = \sum_{k = 0}^{15} {15 \choose k} (2x)^{15-k}\cdot 5^k[/tex]

To find the sixth term, let k  = 5. Therefore, the sixth term is:

[tex]\displaystyle \begin{aligned} z_6 &= {15\choose 5} (2x)^{15-5}\cdot 5^5 \\ \\ & = {15\choose 5}x^{10} \cdot (2)^{10}\cdot 5^5 \\ \\ &= 9609600000x^{10}\end{aligned}[/tex]

Part B)

Likewise:

[tex]\displaystyle \begin{aligned} \left(x^2 + \frac{5}{x}\right)^9 = \sum_{k=0}^9 {9\choose k}(x^2)^{9-k}\left(\frac{5}{x}\right)^{k}\end{aligned}[/tex]

To find the fourth term, let k = 3. Therefore, the fourth term is:

[tex]\displaystyle \begin{aligned} z_4 & = {9\choose 3}\left(x^2\right)^{9-3} \left(\frac{5}{x}\right)^{3} \\ \\ & = {9\choose 3}x^{12} \cdot \frac{5^3}{x^3} \\ \\ & = 10500x^9\end{aligned}[/tex]

A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling the number 2.
If there is more than one element in the set, separate them with commas.

Answers

The sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

What is sample space?

It is defined as the space in which all possible outcomes are represented in a list form for a particular event.

We have:

A number cube with faces labeled from 1 to 6 will be rolled once.

Let S is the sample space:

As we know, the sample space is the set of all possible outcomes:

S = {1, 2, 3, 4, 5, 6}

The total number of outcomes:

n(S) = 6

The outcomes for the event of rolling the number 2.

E = {2}

n(E) = 1

Thus, the sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

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The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold?

Answers

The income that's made based on the equation when 1 comb is sold is $0.5.

How to calculate the price?

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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if f(x) = 4x²-2 then f(-2) is​

Answers

To find f(-2), substitute (-2) into x of the function f(x) = 4x^2-2
We get, f(-2) = 4(-2)^2 - 2
= (4*4)-2 = 16-2 = 14
Therefore, f(-2)=14.

Answer the follwing grade 5 questions of HFC and LCM

Answers

Answer:

give clear image is next question

Step-by-step explanation:

i will give you the answer

How do you solve this?​

Answers

[tex]\text{L.H.S}\\\\=\begin{vmatrix} 1 & bc& b+c\\ 1 & ca& c+a\\ 1 &ab&a+b\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & bc& b+c-(a+b+c)\\ 1 & ca& c+a-(a+b+c)\\ 1 &ab&a+b-(a+b+c)\end{vmatrix}~~~~~~~~~~~~~~~;c_3\rightarrow c_3 -(a+b+c)c_1\\\\\\=\begin{vmatrix} 1 & bc& -a\\ 1 & ca& -b\\ 1 &ab&-c\end{vmatrix}\\\\\\=\dfrac 1{abc}\begin{vmatrix} a & abc& -a^2\\ b & abc& -b^2\\ c &abc&-c^2\end{vmatrix}\\\\\\=-\dfrac {abc}{abc}\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\[/tex]

[tex]=-1\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\\\\\=-1 \times -1 \begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\text{R.H.S}\\\\\text{Showed.}[/tex]

please, I really need this answer the soon as possible. I'm going to be so thankful if anyone could help me with this...​

Answers

Answer:

5/6

Step-by-step explanation:

i'm not rly confident,, but i used a calculator and solved it,,

so im sry if im wrong. Good luck!!

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