Mathematics of inequality
1 answer:
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Answer:
a. 0.82%
b. 71.11%
c. 0.564 micrometer
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
a.
So for 0.62 copies we have:
z = (0.62 - 0.5) / (0.05)
z = 2.4
and this value represents 0.9918
p (x > 0.62) = 1 - 0.9918
p (x > 0.62) = 0.0082 = 0.82%
b.
So for 0.47 copies we have:
z = (0.47 - 0.5) / (0.05)
z = -0.6
and this value represents 0.2742
So for 0.63 copies we have:
z = (0.63 - 0.5) / (0.05)
z = -2.6
and this value represents 0.9953
p (0.47 > x > 0.63) = 0.9953 - 0.2742
p (0.47 > x > 0.63) = 0.7211 = 72.11 %
c.
So for x copies we have:
p = 0.9, It represents z =1.28
1.28 = (x - 0.5) / (0.05)
x = 1.28*0.05 + 0.5
x = 0.564 micrometer
