Given that x is a normal variable with mean μ = 43 and standard deviation σ = 6.5, find the following probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)
Solution :
(a)
P(x 60)
= P[(x - ) / (60 - 43) / 6.5]
= P(z 2.62)
= 0.9956
(b)
P(x 50) = 1 - P(x 50)
= 1 - P[(x - ) / (50 - 43) / 6.5]
= 1 - P(z 1.08)
= 0.1401
(c)
= P[(50 - 43 / 6.5) (x - ) / (60 - 50 / 6.5) ]
= P(1.08 z 2.62)
= P(z 2.62) - P(z 1.08)
= 0.9956 - 0.8599
= 0.1357
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