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Times in the New York City 10K run are normally distributed with a mean of 61...

Times in the New York City 10K run are normally distributed with a mean of 61 minutes and a variance of 81 min2 .

  1. What percentage of runners ran the race between 55 and 70 minutes?
  2. How fast would one have to run in order to be considered one of the fastest 5% of runners?
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Answer #1

 mean = 61

Variance = 81

Sd = sqrt (variance) = sqrt (81) = 9

Hence the percentage of runners ran the race between 55 and 70is

P( 55 < x < 70) = P( x-mean /sd < z < 0) + P(0 < z < x-mean /sd)

= P(55-61/9< z < 0) + P( 0 < z < 70-61/9)

= P(-0.67 <Z < 0) + P( 0 < z < 1.00)

= 0.4525 + 0.3413

P(55 < x < 70) = 0.7938

I. e the percentage of runners ran the race between 55 and 70 is 79.38%.

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