Question

Given that x is a normal variable with mean μ = 107 and standard deviation σ = 11, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 120)


(b)  P(x ≥ 80)


(c)  P(108 ≤ x ≤ 117)

Answer 1

Solution :

(a)

P(x 120)

= P[(x - ) / (120 - 107) / 11]

= P(z 1.18)

= 0.9649

(b)

P(x 80) = 1 - P(x   80)

= 1 - P[(x - ) / (80 - 107) / 11]

= 1 -  P(z -2.45)  

= 0.9929

(c)

= P[(108 - 107 / 11) (x - ) / (117 - 107 / 11) ]

= P(0.09 z 0.91)

= P(z 0.91) - P(z 0.09)

= 0.2827