# probability homework

#### letsstophere

##### New Member
Hello, I am having difficulty figuring out my homework. I made attempts and could someone check my answers and see if I'm right or make suggestions? Thank you

A physical-fitness association is including a mile run in its secondary-school fitness test for boys. The time for this event for boys in secondary school is approximately normally distributed with a mean of 450 seconds and a standard deviation of 40 seconds.

a)What is the probability that a randomly selected boy takes between 420 and 540 seconds to run a mile?

solution: normalcdf(420,540,450,40) = .761 = 76.1%

b)What is the probability that a randomly selected boy takes at least 480 seconds to run a mile?

solution: normalcdf(480,E99,450,40) = .227 = 22.7%

c)What is the probability that a randomly selected boy takes at most 390 seconds to run a mile?

solution: normalcdf(E99,390,450,40) = .0668 = 6.68%

d)If the association wants to designate the fastest 20% as "above average, what time should the association set for this criterion?

e)If the association wants to designate the slowest 5% as "in need of medical evaluation," what time should the association set for this criterion?

Thank you in advance! I am trying!!

#### vinux

##### Dark Knight
a) to c) is look fine.

what s/w you are using? There must be some function for the inverse of the normal probabilities.

d) we have to find value P[time < k seconds] = P[X< k] =.20

e) P[X>k] =.05

#### letsstophere

##### New Member
c)
so you are saying to use the invnorm function?
this is what i tried
invNorm(.80,450,40) = 483.66 seconds
is this correct?

#### vinux

##### Dark Knight
it is d) I don't think that value make sense.
Because fastest mean the lowest time.

Try this.
invNorm(.20,450,40)

#### letsstophere

##### New Member
d)
invNorm(.05,450,40)
=384.206 seconds
could this be it?

#### vinux

##### Dark Knight
No. It is not correct. Do you think slowest and fastest can be identified using same strategy?

Think practically about the values. like "slowest means 384 ? ". Since mean is 450 so it can't be slowest.
This will help to avoid wrong answer.

#### letsstophere

##### New Member
okay i tried invNorm(.20,450,40) = 416.335, is this the answer?

#### vinux

##### Dark Knight
okay i tried invNorm(.20,450,40) = 416.335, is this the answer?
seems fine.

The above is d).

#### letsstophere

##### New Member
As an incentive to improve the fitness of the secondary-school boys for a certain town, a rich benefactor offers a monetary prize to every student. Each student will earn P=640-X dollars, where X is their time in the mile run.

a) What is the mean payout to a secondary-school boy (or, the mean of the random variable P)?

solution: P = 640 - 450 = $190 b) What are the variance and the standard deviations of the payout to a secondary-school boy (or, what are the variance and the standard deviations of the random variable P?) solution: advice needed. #### vinux ##### Dark Knight b) Var(P) = Var(640-X) hint: Var( a+bX) = b^2*Var(X) #### letsstophere ##### New Member i have no clue what you are trying to get me to do. thanks for helping #### letsstophere ##### New Member wait, i went back and did the first question and figured it out kind of e) for the slowest 5% invnorm(.95,450,40) = 515.79 seconds d)the fastest 20% how would i figure this out? #### letsstophere ##### New Member in the variance what would be the "b" #### letsstophere ##### New Member ok i am being confusing i know sorry these are the answers i have so far 1. a) 76.1% b) 22.7% c) 6.68% d) 416.34 seconds (fastest 20%, "above average are faster than 416.34) e) 515.79 seconds (slowest 5%, "in need of medical evaluation") 2. a)P=640-450=$190

and also check my answers! thanks!

#### vinux

##### Dark Knight

Regarding variance. I don't think hint will work for you.
a and b are constant
In your case b = -1 and a =640

Var(640 - X ) = (-1)^2Var(X) = Var(X).=40^2
I hope you know that standard deviation. = sqrt(Var)

Last edited:

#### letsstophere

##### New Member
so you are saying..
the variance is..
-1^2(40^2) = 1600

#### letsstophere

##### New Member
and the standard deviation is
40?

#### vinux

##### Dark Knight
Don't increase the posts in the thread. There is an option for edit.
Yup. You are right.