Heights of women (in inches) are approximately N(64.5,2.5) distributed. Compute the probability that the average height of 25 randomly selected women will be bigger than 66 inches.

Answers

Answer 1
Answer:

Answer:

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Step-by-step explanation:

From the summary of the given statistical dataset

The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:

\mu_(\overline x) = \mu _x = 64.5

\sigma_(\overline x )= (\sigma)/(\sqrt n)

\sigma_(\overline x )= \frac{2.5}{\sqrt {25}}

\sigma_(\overline x )= (2.5)/(5)

\sigma_(\overline x ) = 0.5

Thus X \sim N (64.5,0.5)

Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:

P(\overline X > 66) = P ( (\overline X - \mu_\overline x)/(\sigma \overline x )>(66 - 64.5)/(0.5) })

P(\overline X > 66) = P ( Z>(66 - 64.5)/(0.5) })

P(\overline X > 66) = P ( Z>(1.5)/(0.5) })

P(\overline X > 66) = P ( Z>3 })

P(\overline X > 66) = 1- P ( Z<3 })

P(\overline X > 66) = 1- 0.9987

P(\overline X > 66) =0.0013

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013


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Let F = sin ( 8 x + 5 z ) i − 8 y e x z k . F=sin⁡(8x+5z)i−8yexzk. Calculate div ( F ) div(F) and curl ( F ) . and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Answers

Answer:

Required results are \nabla .\vec{F}=8\cos(8x+5z)-8ye^x[/tex]  and  \nabla* \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}

Step-by-step explanation:

Given vector function is,

\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}

To find\nabla .\vec{F} and \nabla * \vec{F} .

\nabla .\vec{F}

=((\partial)/(\partial x)\uvec{i}+(\partial)/(\partial y) \uvec{j}+(\partial)/(\partial z) \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})

=(\partial)/(\partial x)(\sin(8x+5z))-(\partial)/(\partial z)(8ye^xz)

=8\cos(8x+5z)-8ye^x

And,

\nabla * \vec{F}

=((\partial)/(\partial x)\uvec{i}+(\partial)/(\partial y) \uvec{j}+(\partial)/(\partial z) \uvec{k})*(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})

\end{Vmatrix}

=\uvec{i}\Big[(\partial)/(\partial y)(-8ye^xz)\Big]-\uvec{j}\Big[(\partial)/(\partial x)(-8ye^xz)-(\partial)/(\partial z)(\sin(8x+5z))\Big]+\uvec{k}\Big[-(\partial)/(\partial y)(-\sin(8x+5z))\Big]

=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}

Hence the result.

Assume f(x) = ax^2+ bx + c Which one is true? f is a parabola that opens sideways to the right. f is a parabola that opens sideways to the left. f is a parabola that opens downward. f is a parabola that opens upward.​

Answers

Step-by-step explanation:

f is a parabola that opens upward.

How much more gasoline will it take to fill the tank?

Answers

Answer:

I  think you need to divide both fractions and see if you will get a answer from the answer choices.

Step-by-step explanation:

Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 4 hours. Working alone, it takes the slower worker 6 hours longer to do the job than the faster worker. How long does it take each to do the job alone

Answers

Answer: The faster one needs 6 hours, the slower one needs 12 hours.

Step-by-step explanation:

Let's define Sa and Sb as the times that each worker needs to stuff the envelopes for a political fundraising letter.

Sa is the faster one

Sb is the slower one.

Let's define 1 as a complete task.

Then:

when they both work together, they need 4 hours:

(1/Sa + 1/Sb)*4h = 1.

The slower one needs 6 more hours than the faster one:

Sb = (Sa + 6h).

We can replace this in the first equation and get:

(1/Sa + 1/(Sa + 6h))*4h = 1.

let's solve this for Sa.

1/Sa + 1/(Sa + 6h) = 1/4h.

(Sa + 6h) + Sa = Sa*(Sa + 6h)/4h.

2*Sa + 6h = Sa^2/4h + Sa*(6/4)

Then we have a quadratic equation:

(1/4h)*Sa^2 - (2/4)*Sa - 6h = 0h

(0.25*1/h)*Sa^2 - 0.5*Sa - 6h = 0h

The solutions come from the Bhaskara equation:

Sa = (0.5 +- √((0.5)^2 - 4*0.25h*(-6)) )/(2*0.25* 1/h)  = (0.5 +- 2.5)/(0.5) h

Then we have two solutions:

Sa = ((0.5 + 2.5)/0.5 )h = 6h.

Sb = ( (0.5 - 2.5)/0.5) = -4h

The one that makes sense is the positive option (the negative one has no physical meaning in this situation)

Then the faster worker needs 6 hours to stuff all the envelopes.

And the slower one needs 6h + 6h = 12hours to stuff all the envelopes.

So when they work together, the combined rate is:

(1/6h + 1/12h) = (2/12h + 1/12h) = (3/12h) = (1/4h)

So working together they need 4 hours to stuff all the envelopes.

What is the volume of the cone below

Answers

Answer:

263.99Pi or 264Pi units by approximation

Step-by-step explanation:

Volume of cone is 1/3 x Pi x radius ^2 x height

Radius is given as 6, height as 22

Hence volume of cone= 1/3 x Pi x (6)^2 x 22

=1/3 x PI x36x 22

= 263.99 PI

=264PI units

A new homeowner is mulching a flower bed in his back yard. The flower bed is 9 feet long and 3.5 feet wide. How many square feet will be needed to cover it in mulch?

Answers

Answer:

31.5ft²

Step-by-step explanation:

Formula for area:

Area = Length * Width

Calculate area by substituting in known values

Area = 9 * 3.5

Area = 31.5ft²

31.5ft²

Hope this helps :)