When a mean is 40 and standard dev. is 7.5, how do you find probability that a given value will be greater than 55.75?

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Answer 1 · 2017-07-12T05:58:32

$P_{x > 55.75} = 0.0179$ $P_(x>55.75)=0.0179$

Given -

Mean $μ = 40$ $mu =40$
SD $σ = 7.5$ $sigma=7.5$

At $x = 55.75$ $x=55.75$

$z = \frac{x - μ}{σ} = \frac{55.75 - 40}{7.5} = \frac{15.75}{7.5} = 2.1$ $z=(x-mu)/sigma=(55.75-40)/7.5=15.75/7.5=2.1$

Probability that a given value will be greater than 55.75 = [Area between z=0 and z= $\infty$ $oo$ ] - [Area between z= 0 and z=2.1]

$P_{x > 55.75} = 0.5 - 0.4821 = 0.0179$ $P_(x>55.75)=0.5-0.4821=0.0179$
$P_{x > 55.75} = 0.0179$ $P_(x>55.75)=0.0179$

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