Hey remember Harry from last time. Well as he was working with Jack, another trainer came up to him and relvealed the secrets of the central limit theorem. Harry was so impressed he decided he wanted to crunch some numbers. During these games they have a row off to see how far athletes can row in 4 minutes. At this competition they have an event called "Battle of the North Sea" where athletes are randomly assigned to teams and compete in Viking inspired rowing events. Overall we know that that the average 4 min rowing distance is about 700 meters with a variance of 160000 meters^2, and they know that the distances are not normally distributed.A) For the first event they group into teams of 99 called "Ramming Speed". What percent of teams can average above 730 meters?B) How many standard deviations away from the mean is the target distance for "Ramming Speed"?C) For the second event they group into teams of 31 called "Raiding Party". What percent of teams can average above 730 meters?

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Asked Oct 8, 2019
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Hey remember Harry from last time. Well as he was working with Jack, another trainer came up to him and relvealed the secrets of the central limit theorem. Harry was so impressed he decided he wanted to crunch some numbers. During these games they have a row off to see how far athletes can row in 4 minutes. At this competition they have an event called "Battle of the North Sea" where athletes are randomly assigned to teams and compete in Viking inspired rowing events. Overall we know that that the average 4 min rowing distance is about 700 meters with a variance of 160000 meters^2, and they know that the distances are not normally distributed.

A) For the first event they group into teams of 99 called "Ramming Speed". What percent of teams can average above 730 meters?

B) How many standard deviations away from the mean is the target distance for "Ramming Speed"?

C) For the second event they group into teams of 31 called "Raiding Party". What percent of teams can average above 730 meters?

 

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Expert Answer

Step 1

a.Finding the percentage of teams that can average above 730 meters in the first event:

It is given that the average rowing distance is about 700 meters. That is, μ = 700.  

The population standard deviation is σ = sqrt(16,0000).

The random variable X denotes the rowing distance.

Random sample of 99 (n) teams is considered here.

By central limit theorem for mean, the mean rowing distance follows a normal distribution with mean μ = 700 and standard deviation, 400/sqrt (99) = 40.202.

Thus, the percentage of teams that can average above 730 meters is calculated as follows:

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P(X> 730)1-P(X< 730) EXCEL formulae: NORM DIST(730,700,40.202,TRUE P(X> 730) =1-0.7722 0.2278

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Step 2

Thus, about 22.78% percentage of teams can average above 730 meters in the first event.

b.Finding how many standard deviations away from the mean is the target distance for Ramming speed:

The target distance for Ramming speed is 730 meters.

It is given that the average rowing distance is about 700 meters. That is, μ = 700.  

The standard deviation is σ = 400.

The z-value is given and calculated as follows:

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Z-value -/i 730 700 400 99 0.746

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Step 3

Thus, the target distance for Ramming speed is 0.764 standard deviations above the mean.

c.Finding the percentage of teams that can average above 730 meters in the second event:

Here, by central limit theorem for mean, the mean rowing di...

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P(R>730)1-P(< 730) EXCEL formulae: NORM.DIST (730,700,71.842,TRUE P(X>730) =1-0.6619 0.3381

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