b) Your Statistics teacher has announced that the lower of your two tests will b

Question

b) Your Statistics teacher has announced that the lower of your two tests will be dropped. You got a 90 on test 1 and an 80 on test 2. You're all set to drop the 80 until he announces that the grades ''on curve''. He standardizes the scores in order to decide which is the lower one. If the mean on the first test was 88 with a standard deviation of 4 and the mean on the second test was 75 with a standard deviation of 5,

   i) Which one will be dropped?

   ii) Does this seem ''fair'' ? Explain.

   c) Suppose it takes you 20 minutes, on average, to drive to school, with a standard deviation of 2 minutes. Suppose a Normal model is appropriate of the distributions of driving times.

   i) How often will you arrive at school in less than 22minutes?

   ii) How often will it take you more than 24 minutes?

   iii) Do you think the distribution of your driving times is unimodal and symmetric? Explain.

   iv) What does this say about the accuracy of your predictions? Explain.

Explanation / Answer

b) i) you are within 1 SD of the mean on your first test. You are above one sd from the mean on your second test, so he will drop the first test. ii) This is good for you, you will get a higher final grade. c) i) Everything under one SD above the mean will get you there within 22 min 1-(0.136 +0.0 2.1+.001) = 1 -.158 = 84% of the time. ii)24 min is 2 SD above. So two and more SDs above is 2.1% + 0.1% So 2.2% of the time you will take more than 24 minutes. iii) Driving time is not unimodal and not symmetric. You never go ten times the speed limit, traffic lights stop you for chunks of time, there is less traffic for your mid-day class etc. so the times would be kind of jumpy and there would be at least a distribution around your fast trips and a distribution around you rush-hour trips, so at least bi-modal iv) if the probability distribution isn't Gaussian, the predictions could be off by a lot.

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