# Probability Questions

• Oct 21st 2008, 01:30 PM
AlphaOmegaStrife
Probability Questions
Wasn't sure how to categorize these.

3. Calculate the probability of selecting a college student at random and finding out they have an IQ less than 60 if (a) the probability distribution of the college students IQs is N(64,5) and (b) if the probability distribution is uniform with endpoints 50 and 63.

8. Suppose a computer has 15 main components, each works or does not work independent of the others, with a probability of working equal to 0.8 for each. Now suppose the computer will not boot if 4 or more of the components do not work. Calculate the probability that the computer does not boot.

9. A computer has 1,500 switches, each working or not working independent of the others. Each switch has a probability of 0.6 of working. At least 915 switches must work properly or the computer will not boot. Calculate the probability that this computer boots.

Any help at all would be appreciated. Thanks.
• Oct 21st 2008, 02:50 PM
mr fantastic
Quote:

Originally Posted by AlphaOmegaStrife
Wasn't sure how to categorize these.

3. Calculate the probability of selecting a college student at random and finding out they have an IQ less than 60 if (a) the probability distribution of the college students IQs is N(64,5) and (b) if the probability distribution is uniform with endpoints 50 and 63.

[snip]

(a) $\displaystyle Z = \frac{X - \mu}{\sigma} = \frac{60 - 64}{5} = -0.8$.

Therefore $\displaystyle \Pr(X < 60) = \Pr(Z < -0.8) = \Pr(Z > 0.8) = 1 - \Pr(Z < 0.8)$ by symmetry.

(b) The pdf of X is $\displaystyle f(x) = \frac{1}{13}$ for 50 < x < 63 and zero elsewhere. So $\displaystyle \Pr(X < 60) = \frac{1}{13} \, (60 - 50) = \frac{10}{13}$.
• Oct 21st 2008, 02:53 PM
mr fantastic
Quote:

Originally Posted by AlphaOmegaStrife
[snip]
8. Suppose a computer has 15 main components, each works or does not work independent of the others, with a probability of working equal to 0.8 for each. Now suppose the computer will not boot if 4 or more of the components do not work. Calculate the probability that the computer does not boot.

[snip]

Let X be the random variable number of components that don't work.

X ~ Binomial(n = 15, p = 1 - 0.8 = 0.2).

Calculate $\displaystyle \Pr(X \geq 4) = 1 - \Pr(X \leq 3)$.
• Oct 21st 2008, 03:02 PM
mr fantastic
Quote:

Originally Posted by AlphaOmegaStrife
[snip]
9. A computer has 1,500 switches, each working or not working independent of the others. Each switch has a probability of 0.6 of working. At least 915 switches must work properly or the computer will not boot. Calculate the probability that this computer boots.

Any help at all would be appreciated. Thanks.

Let X be the random variable number of components that don't work.

X ~ Binomial(n = 1500, p = 0.6)

Calculate $\displaystyle \Pr(X \geq 915)$.

You can use the normal approximation to the binomial distribution.