Which of the following functions is graphed below??
2 answers:
Answer:
The required piece-wise function is
Step-by-step explanation:
From the given graph it is clear that it is a piece-wise function because it is braked in two parts.
One part is defined for x≤2 and other part is defined for x>2 because left curve has closed circle at x=2 and right curve has open circle at x=2.
The y-intercept of the function is -3. From the given graph it is clear that the graph defined for x≤2 is a graph of cubic function that shifts 3 units down. So, the required function for x≤2.
From the given graph it is clear that the right curve passes through the point (3,15) and moves towards (2,10).
The function satisfied by both the points. So, the required function for x>2.
Therefore the required piece-wise function is
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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.
To learn more about the normal distribution visit,
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