Z = (score-mean)/SD = ([114-1]-125)/6
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
On the seventh day of Statistics, my teacher gave to me --- seven swans a-swimming. But can they swim faster than American Olympic gold medallist Michael Phelps? Michael can swim the 200 meter butterfly in 1 minute 54 seconds (which is 114 seconds). In the same event, the swim times of the population of swans is normally distributed with a mean time of 125 seconds with a standard deviation of 6. What is the probability that a randomly chosen swan would beat Michael’s Olympic record by 1 second or more? (You might wonder why the swans are so slow. Have you ever seen a swan doing the 200 meter butterfly?)
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