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In the 2014 Winter Olympics, a French skier skied the slalom race in 88.45 seconds and...

In the 2014 Winter Olympics, a French skier skied the slalom race in 88.45 seconds and this time was about one standard deviation faster than the mean. Assuming the race times are normally distributed, about how many of the 34 skiers finishing the event would you expect had a faster race time than the French skier?

(A) 10 (B) 30 (C) 5 (D) 2

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math   Statistics-And-Probability   
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Answer #1

According to empirical law of normal distributions, about 68% of the observations lies within 1 standard deviation of the mean, therefore 32% lies outside one standard deviation and therefore 32/2 = 16% lies on either side of it. Therfore the expected number of skiers finishing the event faster than the 1 standard deviation above mean time is computed here as:

= 16% of 34

= 5.44 which is 5 if rounded to nearest integer.

Therefore c) 5 is the correct answer here.

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