Rectangular distribution (easy question, confusing answer)

[Monkeyseat]

Hi,

Question:

A technique for measuring the density of a silicon compound results in an error which may be modelled by the random variable X, with probability density function:

Find:

a) the value of k,
b) the mean and standard deviation of X.

Working/Solution:

a)

k = 1/(b-a)
k = 1/(0.04 + 0.004)
k = 1/0.08
k = 12.5

b)

E(X) = 0.5(a+b)
E(X) = 0.5(-0.04 + 0.04)
E(X) = 0

Var(X) = (1/12)(b-a)^2
Var(X) = (1/12)(0.04 + 0.04)^2
Var(X) = 1/1875

S.D. = sqrt.(1/1875)
S.D. = 0.0231 to 3 significant figures.

---

I know all is correct, except the standard deviation in part (b). The book says it is 0.031...

Is this a typo, or have I missed something?

Just a quick check. Many thanks.

 

[chivox]

Var(X) = (1/12)(b-a)^2
Var(X) = (1/12)(0.04 + 0.04)^2
Var(X) = 1/1875

S.D. = sqrt.(1/1875)
S.D. = 0.0231 to 3 significant figures.

---

I know all is correct, except the standard deviation in part (b). The book says it is 0.031...

Is this a typo, or have I missed something?

Just a quick check. Many thanks.

Using this formula:

\(\displaystyle SD = \frac{a}{\sqrt{3}}\)

where a = 0.04 in your case (the distribution is rectangular from -0.04 to +0.04), we also get .0231 (.023094) to three sigfigs. This is from the NIST Web site (a US government site: use with caution):

http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc541.htm

If nobody has any other ideas, I would assume it's a typo in the answer key. It happens.

 

[Monkeyseat]

Thanks, I think it's a typo, unless anyone else has anything to say..?