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likoan [24]
2 years ago
8

Suppose you are conducting a survey about the amount grocery store baggers are tipped for helping customers to their cars .for a

similar simulated population with 50 respondents the population mean is $1.73 and the standard deviation is $0.657
about 68% of the sample mean fall with in the intervals $_______ and $________
about 99.7% of the sample mean fall with in the intervals of $-------- and $
Mathematics
1 answer:
ELEN [110]2 years ago
5 0

Using the Empirical Rule and the Central Limit Theorem, we have that:

  • About 68% of the sample mean fall with in the intervals $1.64 and $1.82.
  • About 99.7% of the sample mean fall with in the intervals $1.46 and $2.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

<h3>What does the Central Limit Theorem state?</h3>

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem, the standard deviation of the distribution of sample means is:

s = \frac{0.657}{\sqrt{50}} = 0.09

68% of the means are within 1 standard deviation of the mean, hence the bounds are:

  • 1.73 - 0.09 = $1.64.
  • 1.73 + 0.09 = $1.82.

99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:

  • 1.73 - 3 x 0.09 = $1.46.
  • 1.73 + 3 x 0.09 = $2.

More can be learned about the Empirical Rule at brainly.com/question/24537145

#SPJ1

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Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti
spayn [35]

Answer:

(a)D(x)=-2,500x+60,000

(b)R(x)=60,000x-2500x^2

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500

Therefore, we have:

y=-2500x+b

At point (12,30000)

30000=-2500(12)+b\\b=30000+30000\\b=60000

Therefore:

D(x)=-2,500x+60,000

(b)Revenue

R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0

Therefore:

  • Optimal ticket price:$12
  • Maximum Revenue:$360,000

3 0
3 years ago
A field hockey team wins 80% of its games. Based on your simulation, what is the experimental probability of the team winning it
ElenaW [278]
The probability that they will win their next three games is 51.2%.

The chance that they win is 80%. To find the probability that they win 3 games in a row, we just have to multiply 80% by itself 3 times.

0.8 x 0.8 x 0.8 = 0.512 = 51.2%
6 0
3 years ago
Line AB is tangent to circle O at A. The diagram is not drawn to scale.
Arlecino [84]
AO = 21
BC = 14
OC = radius of the circle = AO = 21
∴ OB = OC + CB = 21 + 14 = 35
<span>Line AB is tangent to circle O at A</span>
∴ AB is perpendicular to AO
∴ Δ OAB is a right triangle at A
Applying Pythagorean theorem
∴  OB² = AO² + AB²
∴ AB² = OB² - AO² = 35² - 21² = 1225 - 441 = 784
∴ AB = √784 = 28
<span />
8 0
3 years ago
What is the quotient (x^3+8)/(x+2)
Citrus2011 [14]

Answer:

Step-by-step explanation:

The easiest way to do this is by using synthetic division (I really hope you know what I'm talking about!)

If the factor is x + 2 = 0, then the solution or the root is x = -2.  We will put -2 outside the "box" and the coefficients from the terms of the polynomial inside the "box":

-2|   1    0    0    8

Bring down the first number and multiply it by the -2.  Put the product up under the first 0 and add:

-2|   1    0    0    8

           -2

      1   -2  

Now multiply the -2 by the -2, put the product up under the next 0 and add:

-2|   1    0    0    8

           -2    4

      1    -2    4

Now multiply the 4 by the -2, put the product up under the 8 and add:

-2|   1    0    0    8

           -2   4    -8

     1    -2   4    0

Those bold numbers are the coefficients to the quotient, which is another polynomial, but is one degree less than the one you started with:

x² - 2x + 4 = 0

Since there is no remainder, then x = -2 is a zero of x³ + 8, and (x + 2) is a factor.

There is a whole world of stuff to learn about quadratics!!

4 0
3 years ago
Kite ABCD is translated (x − 2, y + 3) and then rotated 90° about the origin in the counterclockwise direction. Complete the tab
il63 [147K]

If the resulting coordinate is rotated 90° about the origin in the counterclockwise direction, the final coordinate will be at A'' = (-4, -7), B'' =(-5, -4), C'' = (-4, -3) and D'' =(-3, -4)

Given the coordinate of the vertices ABCD given as

A = (-5, 1)

B = (-2, 2)

C = (-1, 1)

D (-2, 0)

If the coordinates are translated by (x − 2, y + 3), the resulting coordinates will be at:

A' = (-5-2, 1+3) = (-7, 4)

B' = (-2-2, 2+3) = (-4, 5)

C' = (-1-2, 1+3) = (-3, 4)

D' (-2-2, 0+3) = (-4, 3)

If the resulting coordinate is rotated 90° about the origin in the counterclockwise direction, the final coordinate will be at (-y,x)

A'' = (-4, -7)

B'' =(-5, -4)

C'' = (-4, -3)

D'' =(-3, -4)

Learn more on translation here: brainly.com/question/12861087

3 0
2 years ago
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