Enter an equation in point-slope form for the line. Slope is 4 and (−3, −1) is on the line. The equation of the line in point sl
1 answer:
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The final answer is:
a) P( Y < 42.5 ) = 0.8541
b) P( 39.5 < Y < 40.5 ) = 0.1670.
What is the normal distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
If x follows a normal distribution with mean μ and standard deviation σ then the distribution of
follows an approximately normal distribution with a mean
and standard deviation
let x be the height of blades of grass
x follows normal distribution with mean = μ = 4 and standard deviation = σ = 0.75.
Y = x1 + x2 +...........+x10
Distribution of Y is normal with,
Mean = and standard deviation
a)
P( Y < 42.5 )
Using normal distribution formmula,
=NORMDIST( x, mean, SD , 1 )
=NORMDIST(42.5, 40, 2.3717, 1 )
=0.8541
P( Y < 42.5 ) = 0.8541
b)
P( 39.5 < Y < 40.5 ) = P( Y < 40.5 ) - P( Y < 39.5 )
Using normal distribution formmula,
P( Y < 40.5 ) =NORMDIST(40.5, 40, 2.3717, 1 ) = 0.5835
P( Y < 39.5 ) = NORMDIST(39.5, 40, 2.3717, 1 ) = 0.4165
P( 39.5 < Y < 40.5 ) = 0.5835 - 0.4165 = 0.1670
P( 39.5 < Y < 40.5 ) = 0.1670
Hence, the final answer is:
a) P( Y < 42.5 ) = 0.8541
b) P( 39.5 < Y < 40.5 ) = 0.1670.
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Answer:
Yes you can have some peace of mind, because your house is safe. Since, the flagpole is only 14.85 feet, is shorter than the 18 feet of distance from its base to your home.
Step-by-step explanation:
What you need to do is to estimate the height of the pole using its shadow, and the relationship between the height of the fence and it respective shadow:
- <em>For a rectangle triangle, the proportion of its shorter sides are constant</em>.
- <em>The shadows of the fence and of the pole, both form two rectangle triangle.</em>
- <em>The first triangle</em>, the smaller one, <em>has a base of 7 feet</em> (the shadow of the fence), <em>and a height of 4 feet</em> (the corresponding height of the fence)
- <em>The second</em> one, a bigger one, <em>has a base of 26 feet</em> (the shadow of the flagpole), <em>and an unknown height</em> (the height of the pole that its worrying you).
- Then, as stated, the proportion for both triangles remains constant. So:
, where<em> x is the height of the pole.</em>
- x is solved as:
. Meaning that the flagpole has 14.85 feet of height.
- Then when the height is compared to the distance from its base to your home, it is found that the pole is shorter then, there is no risk of the pole falling into your house.