Probability

[TonyHem]

Tasmania Jones is training to throw the javelin for the next Olympic games.
The 'A standard' throwing distance, to be thrown in an authorised competition is 81.80 meters.
The current Olympic record for the men's javelin throw is 90.17 meters.
To be selected for the Olympic games, Tasmania needs to throw the A standard.
Tasmania knows that the distance in metres he can throw the javelin from the marked throwing line follows a normal distribution with mean 80.80 and a standard deviation of 4.50

A) complete the following table correct to 3 decimal places
i) greater than the A standard = 0.412
ii) Greater than the a standard but less than the Olympic Record   = 0.393
iii) Greater than the Olympic Record = 0.019

B) 90% of Tasmania's throws travel at least M meters. Find the value of M, correct to two decimal places.
M = 75.03m

C) Tasmania throws a javelin that does not reach the Olympic Record. What is the probability, correct to 3 decimal places , that it reaches the A standard?
             [I thought this is the same as the 2nd part of the table in part a? Also, how does the normalPDF work? is the difference that this includes the A standard value and the one in part a) is just greater than?]

D) Tasmania's sponsors offer him an incentive to perform his best in competition. The cash rewards for each throw are shown in the table below.
Length of throw                                    |Amount Paid($)|
---------------------------------------------------------|
Under his personal mean                         | 0
Between his personal mean and A standard| 1000
Between A standard and Olympic record    | 2000
Over the olympic record                         | 10,000

D) calculate the expected reward correct to the nearest 10 dollars for Tasmania for each throw he completes in the competition = 1060

E) In a particular competition., Tasmania completes 5 throws,
find:
E)i) - the total reward he would expect to receive, correct to the nearest 10 dollars
5320

ii) The probability, correct to 3 decimal places that at least 3 of the throws will be over the A standard = 0.3384

iii) expected number of times his throw will be over the A standard, correct to 2 decimal places. = 2.06

iv) The probability, correct to 3 decimal places, that Tasmania earns a reward of at least 10,000?


Need help with part C and part E)iV)
Thanks!




JW: is anyone else finding exams 2 a lot harder than exam 1? I'm like getting stuck on so many questions =[

[Damo17]

Tasmania Jones is training to throw the javelin for the next Olympic games.
The 'A standard' throwing distance, to be thrown in an authorised competition is 81.80 meters.
The current Olympic record for the men's javelin throw is 90.17 meters.
To be selected for the Olympic games, Tasmania needs to throw the A standard.
Tasmania knows that the distance in metres he can throw the javelin from the marked throwing line follows a normal distribution with mean 80.80 and a standard deviation of 4.50



C) Tasmania throws a javelin that does not reach the Olympic Record. What is the probability, correct to 3 decimal places , that it reaches the A standard?
             [I thought this is the same as the 2nd part of the table in part a? Also, how does the normalPDF work? is the difference that this includes the A standard value and the one in part a) is just greater than?]



E) In a particular competition., Tasmania completes 5 throws,
find:
E)i) - the total reward he would expect to receive, correct to the nearest 10 dollars
5320

ii) The probability, correct to 3 decimal places that at least 3 of the throws will be over the A standard = 0.3384

iii) expected number of times his throw will be over the A standard, correct to 2 decimal places. = 2.06

iv) The probability, correct to 3 decimal places, that Tasmania earns a reward of at least 10,000?


Need help with part C and part E)iV)
Thanks!

c) Conditional probability


now you already worked out so sub it in.
As for  , in part  a you worked out so . Sub this in and you get 0.4 for the actual answer to part c.



e)iv)For him to get $10000 he need either one throw over the Olympic record or 5 between A standard and Olympic record.

we know that the probability of him throwing over the Olympic record on a given throw is 0.018661 from part a and to get between A standard and Olympic record is 0.393409

So work out each case and add the probabilities together.

For the case of over the Olympic record:





so


For the 5 between A standard and Olympic record.


So the answer to the question is


Note:Forgive the (n/x) stuff, I don't know how to do it on latex.

[kurrymuncher]

JW: is anyone else finding exams 2 a lot harder than exam 1? I'm like getting stuck on so many questions =[

Why would you not find exam 2 harder than exam 1. Its harder, and thats why you're given more time and a calculator. Dont worry, your normal