Question

# Given that x is a normal variable with mean μ = 43 and standard deviation σ...

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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