Probability - Normal distribution

Georgegr

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Hello to everyone. I need help with this problem.
For a random variable X that follows a normal distribution with an unknown mean μ, variance of 2 and P(X<7)=P(X>14), what is the probability P(X<=10)?
The possible answers are:
A. 0.5987 B. 0.5 C. 0.4013 D. 0.8413

I have one equation with one unknown variable, so I can't calculate the asked probability. Any ideas?
 
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Hello to everyone. I need help with this problem.
For a random variable X that follows a normal distribution with an unknown mean μ, variance of 2 and P(X<7=P(X>14), what is the probability P(X<=10)?
The possible answers are:
A. 0.5987 B. 0.5 C. 0.4013 D. 0.8413

I have one equation with one unknown variable, so I can't calculate the asked probability. Any ideas?
That needs to be edited - please fix it.
 
Hello to everyone. I need help with this problem.
For a random variable X that follows a normal distribution with an unknown mean μ, variance of 2 and P(X<7)=P(X>14), what is the probability P(X<=10)?
The possible answers are:
A. 0.5987 B. 0.5 C. 0.4013 D. 0.8413

I have one equation with one unknown variable, so I can't calculate the asked probability. Any ideas?

What equation is that? How are you trying to find the probability?

I would think about P(X<7)=P(X>14) in relation to the symmetry of the normal distribution, and use it to find the mean. Then I'd calculate z and the probability.

Unfortunately, I don't get any of the listed answers. I would, if it were the standard deviation rather than the variance that is 2. Did you copy that correctly?
 
I simply try to calculate it via the tranformation Z=(X-μ)/sqrt(2), but μ is unknown. Actually X~Normal(μ,2).
 
I simply try to calculate it via the tranformation Z=(X-μ)/sqrt(2), but μ is unknown. Actually X~Normal(μ,2).

Did you read what I said?

The statement that P(X<7)=P(X>14) implies what μ is. Think about it! Because the normal distribution is symmetric, under what conditions will two tails on opposite ends be equal?

Only after you see what μ is can you calculate z.
 
Hello to everyone. I need help with this problem.
For a random variable X that follows a normal distribution with an unknown mean μ, variance of 2 and P(X<7)=P(X>14), what is the probability P(X<=10)?
The possible answers are:
A. 0.5987 B. 0.5 C. 0.4013 D. 0.8413

I have one equation with one unknown variable, so I can't calculate the asked probability. Any ideas?

None of the choices seem to be correct.

It should be pretty obvious, (though I guess it wasn't) that \(\displaystyle \mu = \dfrac{7+14}{2} = \dfrac{21}{2}\)

\(\displaystyle \Phi\left(\dfrac{10 - \frac{21}{2}}{\sqrt{2}}\right) \approx 0.361837\)

This isn't listed as a choice.
 
None of the choices seem to be correct.

It should be pretty obvious, (though I guess it wasn't) that \(\displaystyle \mu = \dfrac{7+14}{2} = \dfrac{21}{2}\)

\(\displaystyle \Phi\left(\dfrac{10 - \frac{21}{2}}{\sqrt{2}}\right) \approx 0.361837\)

This isn't listed as a choice.

I was trying to leave it for the OP to realize this; but what you say agrees with what I said in post #3:

Unfortunately, I don't get any of the listed answers. I would, if it were the standard deviation rather than the variance that is 2. Did you copy that correctly?
 
Well I found it! The correct answer is C. The mean is 21/2 and the standard deviation is 2. Thank's for your help. Finally, it was easy...
 
Well I found it! The correct answer is C. The mean is 21/2 and the standard deviation is 2. Thank's for your help. Finally, it was easy...

I assume you're saying that you misquoted the problem when you said the variance was 2?

Actually, since 10 is less than the mean and C was the only answer less than 0.5, I guessed it even before I did any calculations -- but then the details made even that answer wrong, so we had to ask. So, yes, the answer was easy once the problem was correct.
 
I simply try to calculate it via the tranformation Z=(X-μ)/sqrt(2), but μ is unknown. Actually X~Normal(μ,2).

The correct way to use this notation is \(\displaystyle X \thicksim N(\mu , \sigma^2)\), where the second parameter is variance.

Unfortunately, I have seen, in more than one textbook \(\displaystyle X\thicksim~N(\mu, \sigma)\), where the second parameter is standard deviation.

Maybe this was the issue here, or else the answer given was simple incorrect.
 
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