This graph shows the linear relationship between the time in seconds, x, for Caroline's walk and the distance in meters, y, Caro
line is from her starting point. The graph passes through the point (20,30). According to the graph, how many meters will Caroline walk in exactly one hour?
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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