The time needed to complete a final examination is normally distributed with a m

Question

The time needed to complete a final examination is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. A. What is the probability of completing the exam in one hour or less? B. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (i.e., between 60 and 75 minutes)? C. The maximum time allowed for writing the exam is 90 minutes. What is the percentage of students do you expect to be unable to finish the exam within the allowed time?

Explanation / Answer

for normal distribution z=(X-mean)/std deviation

A)probability of completing in one hour or less =P(X<60)=P(Z<(60-80)/10)=P(Z<-2)=0.0228

B)P(60<X<75)=P((60-80)/10)<Z<(75-80)/10)=P(-2<Z<-0.5)=0.3085-0.0228=0.2858

C)P(X>90)=1-P(X<90)=1-P(Z<(90-80)/10)=1-P(Z<1)=1-0.8413=0.1587

therefore 15.87% students will not be able to finsih with in the schedule time,

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