# Thread: Hi, new here! Was wondering if I am right, I would

1. ## Hi, new here! Was wondering if I am right, I would

I would rather try things out as far as they can go, and then ask for help!

I am having problems on a statistics problem, that goes like this:

Suppose that a random variable X observes normal distribution N~(58.2, 12.55).

1)Calculate P(X>25)

For this I find the z-score. Z=X-M/S, X=random variable, M=mean, S=standard deviation. So, Z=X-M/S = 25-58.2/12.55= -2.65. This is where I am confused. After this I have P(X>25)= 0.50-P(-2.65<X<0)= 0.004. I am not sure if I am right on this.

The second part of the question, still keeping the same mean and standard deviation, goes like this:

Calculate P(49.6<X<65.3) I converted each X into a z-score:

Z=65.3-58.2/ 12.55= 0.56
Z=49.6-58.2/ 12.55= -0.69

Then I looked up each z-score in a normal table in my statistics book to find the percentage that corresponds to each z-score: (Did I do my notation right, by the way?)

For z-score 0.56: P(0<X<0.56)= 0.2123
For z-score -0.69: P(0<X-0.29)= 0.1141

Finding z-scores then looking in a normal table to find percentages/probability is easy, but I get lost here. I don't know how to "complete" the problem and answer what is being asked of me. Help please? What am I lost on?

2. Originally Posted by peanutbutter
I would rather try things out as far as they can go, and then ask for help!

I am having problems on a statistics problem, that goes like this:

Suppose that a random variable X observes normal distribution N~(58.2, 12.55).

1)Calculate P(X>25)

For this I find the z-score. Z=X-M/S, X=random variable, M=mean, S=standard deviation. So, Z=X-M/S = 25-58.2/12.55= -2.65. This is where I am confused. After this I have P(X>25)= 0.50-P(-2.65<X<0)= 0.004. I am not sure if I am right on this.

[snip]
1) Your answer is wrong. Since 25 is much less than the mean value of 58.2, you would certainly expect Pr(X > 25) to be greater than 0.5 and in fact you should expect the answer to be quite close to 1 since 25 is more than two standard deviations away from the mean .....

Pr(X > 25) = Pr(Z > -2.65) = Pr(Z < 2.65) by symmetry.

So your answer should be 1 - 0.004 = 0.996 (assuming you're using tables).

I'll get to the second part later.

3. Originally Posted by peanutbutter
The second part of the question, still keeping the same mean and standard deviation, goes like this:

Calculate P(49.6<X<65.3) I converted each X into a z-score:

Z=65.3-58.2/ 12.55= 0.56
Z=49.6-58.2/ 12.55= -0.69

Then I looked up each z-score in a normal table in my statistics book to find the percentage that corresponds to each z-score: (Did I do my notation right, by the way?)

For z-score 0.56: P(0<X<0.56)= 0.2123
For z-score -0.69: P(0<X-0.29)= 0.1141 Mr F says:

Finding z-scores then looking in a normal table to find percentages/probability is easy, but I get lost here. I don't know how to "complete" the problem and answer what is being asked of me. Help please? What am I lost on?
Note that Pr(49.6 < X < 65.3) = Pr(-0.69 < Z < 0.56) = Pr(-0.69 < Z < 0) + Pr(0 < Z < 0.56) = Pr(0 < Z < 0.69) + Pr(0 < Z < 0.56) = ........