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4 years ago

12

A population is normally distributed with µ = 100 and σ = 10. a sample of size 9 is selected. the probability that an individual

value (from this population) falls between 90 and 110 will be ________ the probability that the sample mean (of this sample) falls between 90 and 110.

1 answer:

ASHA 777 [7]4 years ago

7 0

A) The empirical rule tells you the probability of being within 1 standard deviation of the mean is 68%.

b) The probability that the sample mean falls within 3 standard deviations* of the mean is 99.7%.

___
* The standard deviation of the sample mean is 1/√9 = 1/3 of the standard deviation of an individual sample. Hence the same limits (90-110) now cover 3 standard deviations of the sample mean.

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What is 0.0728 correct to two significant figures?

katen-ka-za [31]

0.073.

2SF is 2 numbers excluding preliminary zeros,

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4 years ago

What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

<h2>2x + 3y = 5</h2>

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ <em>subtract 2x from both sides</em>

$3y=-2x+6$ <em>divide both sides by 3</em>

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ <em>subtract 4/3 from both sides</em>

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ <em>multiply both sides by 3</em>

$3y=-2x+5$ <em>add 2x to both sides</em>

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines <em>k</em> and <em>l</em> are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

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Answer:

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Step-by-step explanation:

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3 years ago

Jack’s bicycle tires have a diameter of 24 inches. If he rides at 15 miles per hour, what is the angular velocity of the wheels

Oksanka [162]

Answer:

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Step-by-step explanation:

The relation between the angular velocity ω and the linear velocity v is v=ωr

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Converting ω from rad per minutes to revolutions per minute

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