1) The time needed to complete a test in a particular college course is normally

Question

1) The time needed to complete a test in a particular college course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes. Answer the following questions.

Please include exactly what to type into Excel to get the answers in the spreadsheet.

a) What is the probability of completing the test in one hour or less?

b) What is the probability that a student will complete it in more than 60 minutes but less than 105 minutes?

c) Assume that the class has 60 students and that the testing period is 120 minutes in length. How many students do you expect will be unable to complete the test in the allotted time?

Explanation / Answer

X: Time needed to complete a test in a particular college course

X~ N(90,225)

a) P[ X<=60 ]=P[ (X-90)/15 <= (60-90)/15 ]= P[ Z <= -2] = 0.0228 {using minitab & cumulative probability}

b) P[60<X<105]= P[X<105] - P[X<60] = P[X-90/15< (105-90)/15] - P[X-90/15< (60-90)/15]=P[Z<1] - P[Z< -2]

=0.841345 - 0.0227501 = 0.81859

c) P[X>120] = P[ X-90/15 > (120-90)/15] =P[Z> 2] = 1- P[Z<2] =1- 0.977250 =0.02275.

So No of students expected to be not able to finish is 60* 0.02275= 1.365 or approx 1.

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