# Thread: Mathematical statistic? Random variable, normal distribution, standard deviation?

1. ## Mathematical statistic? Random variable, normal distribution, standard deviation?

Say X a random variable that satisfies a normal distribution

E(X) = 15, the standard deviation is 3.

1) Write down the density function of X.
y = e^(−½(x−15)²/3²) / √[ 2π3² ]
y = e^(−(x−15)²/18) / √[ 18π ]

2) Compute P(X <= 18)
18 − 15 = 3
3 / 3 = 1
P(Z<1) = 84.13%

3) Compute P(X >= 21)
P(X>21)
21 − 15 = 6
6 / 3 = 2
P(Z>2) = 2.27%

4) Compute P(11 <= X <= 19)
P(11<X<19)
11 − 15 = −4
Z₂ = −4 / 3 = −1.333
19 − 15 = 4
Z₁ = 4 / 3 = 1.333
P(−1.333<Z<1.333) = 81.75%

Can someone verified if these are 100% correct? Thanks, you need a table for this problem though.

2. Originally Posted by dkmathguy
Say X a random variable that satisfies a normal distribution

E(X) = 15, the standard deviation is 3.

1) Write down the density function of X.
y = e^(−½(x−15)²/3²) / √[ 2π3² ]
y = e^(−(x−15)²/18) / √[ 18π ]

2) Compute P(X <= 18)
18 − 15 = 3
3 / 3 = 1
P(Z<1) = 84.13%

3) Compute P(X >= 21)
P(X>21)
21 − 15 = 6
6 / 3 = 2
P(Z>2) = 2.27%

4) Compute P(11 <= X <= 19)
P(11<X<19)
11 − 15 = −4
Z₂ = −4 / 3 = −1.333
19 − 15 = 4
Z₁ = 4 / 3 = 1.333
P(−1.333<Z<1.333) = 81.75%

Can someone verified if these are 100% correct? Thanks, you need a table for this problem though.
I cannot stand answers to questions like these expressed as a percentage. You should be giving a number correct to four decimal places that lies between 0 and 1.

Having said this, your answers are correct (taken with a grain of salt), except:

I get 0.0228 for #3, correct to four decimal places (which I suppose you would want to write as 22.28% ....).
I get 0.8176 for #4, correct to four decimal places (which I suppose you would want to write as 81.76% ....).

3. Thanks mr fantastic for verifying this. I will write my answer to 4 decimal places form now on.