Question 826561: Please help me solve this problem:
In a driving school, the time taken by student drivers to complete a full circuit of the test course was found to be normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.
(i) What proportion of students will complete the circuit in one hour?
(ii) How long should the driving lessons last so that 95% of students will have finished the circuit by the end of their lesson?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a driving school, the time taken by student drivers to complete a full circuit of the test course was found to be normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.
(i) What proportion of students will complete the circuit in one hour?
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z(60) = (60-45)/10 = 1.5
P(x <= 60) = P(z < 1.5) = normalcdf(-100,1.5) = 0.1295 = 1295/10,000
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(ii) How long should the driving lessons last so that 95% of students will have finished the circuit by the end of their lesson?
invNorm(0.95) = 1.645
Use x = z*s+u
time = 1.645*10+45 = 16.45+45 = 61.45 minutes.
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Cheers,
Stan H.
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