Question on statistics. Probability of a jump within one standard deviation of the mean

[webnewland]

Here is the question:
The Probability distribution function of jumping a distance of x meters is given by:
f(x) = (pi/20)*sin(pi*x/10)
where 0 < x < 10

What is the probability of the jump is within one standard deviation of the mean?

Here is some information i already gathered:
Mean: 5
Median: 5
Standard deviation: 2.1762
variance: 4.7358

I am thinking this is how the answer should be solved, but not entirely sure about it.

Integral of (pi/20)*sin(pi*x/10) Evaluated from (5-2.1762) to (5+2.1762), which is evaluated from 2.8238 to 7.1762
Rendering the answer to be 0.6316

Can anyone let me know if i am doing it correctly? if not, what is wrong?
Thanks a ton

 

[webnewland]

can anyone help?

 

[MacBaine]

 

[goodoptics]

<< Here is the question:
The Probability distribution function of jumping a distance of x meters is given by:
f(x) = (pi/20)*sin(pi*x/10)
where 0 < x < 10

What is the probability of the jump is within one standard deviation of the mean?

Here is some information i already gathered:
Mean: 5
Median: 5
Standard deviation: 2.1762
variance: 4.7358

I am thinking this is how the answer should be solved, but not entirely sure about it.

Integral of (pi/20)*sin(pi*x/10) Evaluated from (5-2.1762) to (5+2.1762), which is evaluated from 2.8238 to 7.1762
Rendering the answer to be 0.6316

Can anyone let me know if i am doing it correctly? if not, what is wrong?
Thanks a ton >>



You logic sounds right to me and .6316 sounds resonable.

 

[silverpig]

You got it.