In the given normal distribution of having the μ = 50 and σ = 10, determine the probability that x assumes have the values in between 45 and 62.

In the given normal distribution of having the μ = 50 and σ = 10, determine the probability that x assumes have the values in between 45 and 62.

Solution:

Getting the z values will correspondence to the x1 = 45 and x2 = 62

Z1  = 45 – 50 = -0.5

            10

And

X2 = 62 – 50 = 1.2

            10

Therefore,

P (45< x < 62) = P(-0.5 < z , 1.2).

 

 

The P (-0.5 < z < 1.2) is shown through the area of the shaded region. This area can be found by the difference of the area of the left to the ordinate of the z = -0.5 from the whole area to the left of the z = 1.2. This means we have:

P(45< x < 62) = P (-0.5 < z < 1.2)

                         = P (z < 1.2) – P (z< -0.5)

                         = 0.8849 – 0.3085

                         = 0.5764

Credit:ivythesis.typepad.com

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