Question

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)

Answer #1

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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