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.I have already found A-D, I need help on how to figure out E.A) For the first event they group into teams of 99 called "Ramming Speed". What percent of teams can average above 730 meters? 0.2278B) How many standard deviations away from the mean is the target distance for "Ramming Speed"? 0.7462C) For the second event they group into teams of 31 called "Raiding Party". What percent of teams can average above 730 meters? 0.3381D) How many standard deviations away from the mean is the target distance for "Raiding Party"? 0.4176E) Jack (remember he was the promising athlete from last time) wants to know what his teams average should be if they want to get into the top 5% both the "Ramming Speed" and "Raiding Party" events. "Ramming Speed"="Raiding Party"=

Question
Asked Oct 9, 2019

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.

I have already found A-D, I need help on how to figure out E.

A) For the first event they group into teams of 99 called "Ramming Speed". What percent of teams can average above 730 meters? 0.2278

B) How many standard deviations away from the mean is the target distance for "Ramming Speed"? 0.7462

C) For the second event they group into teams of 31 called "Raiding Party". What percent of teams can average above 730 meters? 0.3381

D) How many standard deviations away from the mean is the target distance for "Raiding Party"? 0.4176

E) Jack (remember he was the promising athlete from last time) wants to know what his teams average should be if they want to get into the top 5% both the "Ramming Speed" and "Raiding Party" events.
"Ramming Speed"=
"Raiding Party"=

check_circleExpert Solution
Step 1
  1. E) It is provided that the average rowing distance is about 700 meters, that is, μ = 700.  

The population standard deviation is σ = sqrt(16,0000) = 400.

Consider a random variable X denotes the rowing distance which follows normal distribution.

The sample size for “Ramming Speed” is 99 and for “Raiding Party” is 31.

Step 2

Jack wants to know the average to get into the top 5% for both the events. ...

P(X> 0.05
1-P(X)- 0.05
P(Xs) 0.95
x-700
Ф
0.95
400
99
T700 (0.95)
400
99
T-700
(Using Excel finction -NORMSINV (
0.8289
11
400
99
733.323 meters
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P(X> 0.05 1-P(X)- 0.05 P(Xs) 0.95 x-700 Ф 0.95 400 99 T700 (0.95) 400 99 T-700 (Using Excel finction -NORMSINV ( 0.8289 11 400 99 733.323 meters

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