This year, the ACT score of a randomly selected student is normally distributed with a mean of 24.4 points and a standard deviation of 4.7 points. Let XX be the ACT score of a randomly selected student and let ¯¯¯XX¯ be the average ACT score of a random sample of size 16.

1. Describe the probability distribution of XX and state its parameters μμ and σσ:

Answers

Answer 1

The probability distribution of the sample mean is approximately normal, with mean of 24.4 points and standard deviation of 1.175 points.

How to obtain the distribution?

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: $s = \frac{\sigma}{\sqrt{n}}$.

The mean is the same as the population mean, of 24.4 points, while the shape is approximately normal.

The standard error is given as follows:

$s = \frac{4.7}{\sqrt{16}} = 1.175$

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Related Questions

y = x - 10
is this a linear function

Answers

Answer:

Step-by-step explanation:

Yes, because it's a straight line when you plot that equation.

Yes it is BC it is all in a straight line if you were to plot it

ariana has $1.40 worth of nickels and dimes. she had twice as many nickels as dimes. determine the number of nickels and the number of dimes that ariana has

Answers

Answer:

Ariana has 7 dimes and 14 nickels

Step-by-step explanation:

Nickel = 0.05

Dime = 0.10

1.40 ÷ 2 = 0.70

7 x 2 = 14

because Adriana has twice the nickels as dimes and half of the 1.40 is dimes so the other half is nickels.

nickels x 2 = 14

Taylor has xx nickels and yy dimes, having no less than 15 coins worth a maximum of $1 combined. At least 14 of the coins are nickels. Solve this system of inequalities graphically and determine one possible solution.

Answers

Answer:

Step-by-step explanation:

The system of inequalities can be written as follows:

x ≥ 14

x + y ≥ 15

0.5x + 0.1y ≤ 1

We can graph the system by plotting the three lines representing the three inequalities.

The first inequality, x ≥ 14, is a vertical line with x-intercept at (14, 0).

The second inequality, x + y ≥ 15, is a line with a slope of 1, passing through the point (0, 15) and with y-intercept at (0, 15).

The third inequality, 0.5x + 0.1y ≤ 1, is a line with a slope of -5, passing through the point (2, 0.2) and with y-intercept at (0, 0.2).

The solution to the system of inequalities is the region below the line representing the first inequality, above the line representing the second inequality, and to the right of the line representing the third inequality.

One possible solution is x = 16 and y = 1. This means that Taylor has 16 nickels and 1 dime, which is exactly 15 coins worth a maximum of $1 combined.

Answer: the person is right above just made sure that .5 is .05 since it’s cents. A nickel is worth .05 cents not .5 cents.

Step-by-step explanation:

Q2) For the following exercises, write the first five terms of the indicated
sequence:

Answers

The first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.

To find the first five terms of the sequence aₙ = 3n/(n+4)

we need to substitute the values of n from 1 to 5 and solve for .

a₁ = 3×1/(1+4) = 3/5

a₂ = 3×2/(2+4) = 3/4

a₃ = 3×3/(3+4) = 9/7

a₄ = 3×4/(4+4) = 12/8 = 3/2

a₅ = 3×5/(5+4) = 15/9

Hence, the first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.

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The value of a baseball player's rookie card began to increase once the player retired. When he retired in his card was worth $. The value has increased by $ each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in ?

Answers

No, x an y are not proportional and the value of card in 2006 is $38.05.

Given that when the value of card was $8.24 and the value has increased by $2.71 each year.

We are required to find the value of card in 2006 and tell whether the relationship between x and y are proportional or not.

When he retired in 1995, the value of card=$8.24

Value increased each year=$2.71

y=Value of card

x is number of years from the year of retirement

According to question, the equation will be as under:

y=2.71x+8.24

We have to use the value of x be 1 in the above equation.

y=2.71*1+8.24

y=2.71+8.24

y=10.95

Substituting x=2 in the equation.

y=2.71*2+8.24

y=13.66

If x and y are proportional then,

$x_{1} /y_{1} =x_{2} /y_{2}$=k=constant

1/10.95≠2/13.66

To find the value of card in 2006 we have to put the value of x=11 in the equation.

y=2.71*11+8.24=38.05

Hence x and y are not proportional and the value of card in 2006 is $38.05.

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Question is incomplete as the following should be included:

The value of card was $8.24 and we have to find the value of card in 2006.

How do you divide fast without a calculator?

Answers

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Find the midpoint of the segment with the given endpoints.
(3,- 9) and (4, -8)

Answers

(3,-9)(4,-8)

$\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\\ \sf\longmapsto \left(\dfrac{3+4}{2},\dfrac{-9+8}{2}\right)$

$\\ \sf\longmapsto \left(\dfrac{7}{2},\dfrac{-1}{2}\right)$

A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a group of 50 mothers, the following information was obtained. Let X = the number of times a newborn wakes its mother after midnight. For this example: x = 0, 1, 2, 3, 4, 5. It was found that 2 children didn't wake their moms at all, 11 woke her once, 23 woke her twice, 9 woke her 3 times, 4 woke mom 4 times, and 1 woke mom 5 times. Remember, P(x) = probability that X takes on a value of x
1) Create a PDF Table.
2) How do you know this is a PDF?
3) How do you know this is a discrete PDF?

Answers

The probability density function (PDF) table for the number of times a newborn baby wakes its mother after midnight is as follows:

x = 0: P(x) = 2/50 = 0.04

x = 1: P(x) = 11/50 = 0.22

x = 2: P(x) = 23/50 = 0.46

x = 3: P(x) = 9/50 = 0.18

x = 4: P(x) = 4/50 = 0.08

x = 5: P(x) = 1/50 = 0.02

1) A probability density function (PDF) table is created by listing the possible values of the random variable (in this case, the number of times a newborn wakes its mother after midnight) and their corresponding probabilities. The table shows the probabilities for each value of x, where x represents the number of times the newborn wakes the mother.

2) This is a PDF because the probabilities listed in the table are non-negative and sum up to 1. The probabilities represent the likelihood of each possible outcome occurring. In this case, the probabilities represent the likelihood of the baby waking the mother a certain number of times after midnight.

3) This is a discrete PDF because the random variable, the number of times the newborn wakes the mother after midnight, can only take on specific integer values (0, 1, 2, 3, 4, or 5). The probabilities assigned to each value represent the likelihood of that particular outcome occurring. Discrete PDFs are used when the random variable is discrete and can only assume certain distinct values.

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Which pair of angles is not congruent?

Answers

Answer:

D.
hope it helps with your work! x

If x ≠ 0, then x²/2x⁵ × 1000 is equivalent to

Answers

Answer:

Not telling you the answer that just the steps, that would be cheating.

Step-by-step explanation:

1. Mulitply 1000 by the fraction.

2. Simplify it(the numbers 1000 and 2 to 500 and 1)

3. Then divide the exponents(you know this I taught you:)

4. You then will get your answer! (hint: it has a negative exponent :)

5. Please try not to use Brainly next time, try it yourself:) or I may take points off, ask me next time.

8. If a conditional is true and its hypothesis is true, then its_____ is true.

Answers

Answer: Conclusion

If a conditional is true and its hypothesis is true, then its conclusion is true.

The 5th and 9th terms of a geometric sequence are 1,280 and 327,680, respectively. Which term of this sequence is 5,242,880? n =

Answers

The term of the sequence that equals 5,242,880 is the 16th term. The given geometric sequence has a common ratio, r, which can be determined using the 5th and 9th terms. Then, by setting up an equation to find the term that corresponds to the value 5,242,880, we can solve for n.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio (r). Given that the 5th term is 1,280 and the 9th term is 327,680, we can use these values to determine the common ratio. We can find the common ratio by dividing the 9th term by the 5th term:

327,680 / 1,280 = r^4,

simplifying to:

256 = r^4.

Taking the fourth root of both sides, we find:

r = 2.

Now that we know the common ratio, we can set up an equation to find the term that corresponds to the value 5,242,880:

1,280 * 2^(n-1) = 5,242,880.

Solving this equation for n:

2^(n-1) = 5,242,880 / 1,280,

2^(n-1) = 4,096.

Taking the logarithm base 2 of both sides:

n - 1 = log2(4,096),

n - 1 = 12.

Solving for n, we find:

n = 13.

Therefore, the term of the sequence that equals 5,242,880 is the 16th term (n = 13 + 1 = 14).

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Suppose you have an isosceles triangle with a 90° angleIf the congruent sides each measure 9 feet, what is the length of the side across from the right angle?

Answers

Answer:

$9\sqrt{2}$ feet

Step-by-step explanation:

Consider the attached figure.

An isosceles triangle is a triangle in which two sides are equal.

$AB=BC=9$ feet

According to Pythagoras theorem,

square of hypotenuse is equal to sum of squares of other two sides.

$AC^2=AB^2+BC^2\\AC^2=9^2+9^2\\AC^2=81+81\\AC^2=162\\AC=\sqrt{162}$

$AC=9\sqrt{2}$ feet

Evaluate f(-6) for the
function f(x) = 3 - 2x

Answers

Answer:

Step-by-step explanation:

Replace each instance of 'x' with '(-6):'

f(-6) = 3 - 2(-6)

= 3 + 12 = 15

Darrell writes 15 text messages in 5 minutes. What is the minutely rate?

Answers

The answer is 3 messages per minute.

If you do the work, 1 times 15 divided by 5= 3. Or 5 times 3= 15.

Darrell writes 15 text messages in 5 minutes. What is the minutely rate?

What are these as equalivalent equations

Answers

Answer:

6x - 2(x - 3) and x + 3(x - 2) - 6

The two expresaions that are quivalent are 6x - 2(x - 3) and x + 3(x - 2) - 6.

Step-by-step explanation:

First expression which is 4(x - 3) is an example of a binomial that when multiplied together, the product would be 4x - 12. Therefore, second and third expressions are the answer.

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When you use your Taylor polynomial to estimate the probability that a value lies within two standard deviations of the mean, what do you get

Answers

When using a Taylor polynomial to estimate the probability that a value lies within two standard deviations of the mean, the result will depend on the specific function used to create the polynomial. However, in general, a Taylor polynomial can provide a good approximation of the function within a certain interval.

1. Identify the function: The probability distribution function for a normal distribution is given by the function f(x) = (1/σ√(2π)) * e^(-(x-μ)^2 / 2σ^2), where μ is the mean and σ is the standard deviation.

2. Determine the interval: Two standard deviations from the mean are represented by the interval [μ - 2σ, μ + 2σ].

3. Apply Taylor polynomial: Approximate f(x) using a Taylor polynomial centered at μ. The higher the degree of the polynomial, the more accurate the approximation.

4. Calculate probability: Integrate the Taylor polynomial over the interval [μ - 2σ, μ + 2σ] to estimate the probability.

5. Interpret the result: The estimated probability represents the likelihood that a value lies within two standard deviations of the mean in a normal distribution.

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a shipment to a warehouse consists of 4,000 MP3 players. The manager chooses a random sample of 50 MP3 players and finds 4 that are defective. How many MP3 players in the shipment are likely to be defective?

Answers

Answer:

320

Step-by-step explanation:

Answer:

320 MP3 players

Step-by-step explanation:

4/50 MP3 players are defective

Multiply by 80 to get the whole shipment

4/50 x 80 = 320/4000

what is the slope of the line that goes through 11,2 and 14,16

Answers

Step-by-step explanation:

m = y2-y1/x2-x1

m = 16 - 2/ 14 - 11

m = 14/3

m = 14 / 3

Hope it helps.

Leila bought lunch at school. She had a sandwich and a shake that cost her $8. Her shake cost
$3.75. Solve the equation 8 =s +3.75 to find the cost of Leila's sandwich, s.

Answers

Answer: I think that the sandwich is $4.25 (I'm not sure)

Answer:

s=4.25

Step-by-step explanation:

look at the screenshot for the steps! :)

The vertices of triangle PQR are P(3,4), Q(5,8) and R(7,4). Find the length of QS and deduce the area of the triangle PQR

Answers

Check the picture below.

The vertices of triangle PQR are P(3,4), Q(5,8) and R(7,4). Find the length of QS and deduce the area

On the first day, 8 adult tickets were sold and 13 student tickets were sold for a total of $75. On day two, 10 adult tickets were sold and 9 student tickets were sold for a total of $72. What is the cost of an adult ticket? What is the cost of a student ticket?

Answers

Step-by-step explanation:

8x + 13y = 75 (×10)

10x + 9y = 72 (×8)

80x + 130y = 750

-) 80x + 72y = 576

58y = 174

y = 3

10x + 9(3) = 72

10x + 27 = 72

10x = 72 - 27

10x = 45

x = 4.5

adult = $4.50

student = $3

Roselyn is driving to visit her family, who live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0. 60 0. 600, point, 60 dollars per liter.

Answers

She can drive 2 hours before she runs out of fuel and needs 5 liters of more fuel to complete her journey. The price for the amount of fuel that Roselyn will use for the entire drive is $25

Calculation:

Total distance = 150km

Average speed = 60km/h

Total fuel = 20 L

Fuel efficiency = 6km/l

The car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter.

Total distance she can drive with 20L fuel in her car's tank = 6*20 = 120km

Time taken to cover 120 km = 120/60

Time taken = 2 hours

Therefore, She can drive 2 hours before she runs out of fuel.

Distance left to travel = 150 - 120

= 30km

To travel 30 km, extra fuel needed = Distance/Fuel efficiency = 30/6

= 5 liters

The cost of the fuel is $0.60/L

For 5km, extra fuel would cost her 0.60*5 = $3

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PLEASE HELP ME ITS DUE TMR
THANK YOU!

Answers

Answer:

18. 24%

19. $60.75

Step-by-step explanation:

18. You have to divide the change by the original number to find percent change. In this case you need to do 12/50 = 0.24. Therefore, the discount is 24%.

19. You have to multiply the original price by 0.25 to find how much the discount costs, then decrease the discount cost from the original price, which in this case is 90*0.25 = 22.50, you then have to decrease the sales price by 10% so you have to repeat the same thing with 0.1, so 67.5*0.1 = 6.75, 67.5- 6. 75 = 60.75. The final price is $60.75.

Which of the following situations can be represented by
C = 10 + 0.44n?
Your answer:
A. The total cost at the grocery store for a cake that cost $10 and n bananas that cost $0.44 each.
B. The total cost of 10 soft drinks that cost $0.44 each.
C. The height of a plant after n days that was 10 centimeters tall and it grew 4.4 milimeters a day.
D. Not here

Answers

Answer:

A and C

Step-by-step explanation:

I need help ASAP!! Please only answer if you know the answer, not if you don't.
2x - 1/4x= -28

Answers

Answer:

x = -16

Step-by-step explanation:

2x - 1/4x= -28

2x - 0.25x= -28

1.75x = -28

1.75x/1.75 = -28/1.75

x = -16

Is this answer right

Answers

Answer: No the real answer is 35.10585

Step-by-step explanation:

PLEASE HELP ME!!! 30 points to the first person that can answer!

The area of a triangle is 225 square feet. The height of the triangle is half of its base. How many feet is the base?