The time needed to complete an exam is normally distributed with (M,O^2) . a. If

Question

Explanation / Answer

Let Mean time be x and Standard deviation be S.D

Z equivalent for 2.28%=-2

Z equivalent for 93.32% (100-6.68)=1.5

(1)

2.28% of the class can expect to complete the exam within an hour or less (60 min or less)

(x-60)/S.D =2

Or x=2*S.D+60

(2)

6.68% of the class need more than an hour and 35 minutes to complete the same exam (95 min or more)

(95-x)/S.D=1.5

X=95-1.5*S.D

Form (1) and (2)

2*S.D+60=95-1.5*S.D

3.5*S.D=35

S.D=35/3.5=10min

Putting S.D in (1)

X=2*S.D+60=2*20+60=80min

Thus Average time to complete the eam =80 min=1 hour and 20 min

Standard deviation = 10 min

Probability for student completing the exam in more than 60 min(1hour) and less than 75 min (1.25 hour)

Z value for 60 min=(60-80)/10=-2

Z value for 75 min=(75-80)/10=-0.5

Probabilty=P(z=-0.5)-P(z=-2) =0.3085-0.0228=0.2857

Probability for student completing the exam in more than 1hour and less than 1.25 hour=28.57%

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