Chapter 4, Problem 143ACB

(a)

To determine

Prove that the probabilities for x in the table sum to 1.

(b)

To determine

Compute the probability that 3 or 4 of the homes in the sample have a dust mite level that exceeds $2\mu g/g$.

(c)

To determine

Obtain the probability that fewer than two homes in the sample have a dust mite level that exceeds $2\mu g/g$.

(d)

To determine

Compute $\mu =E\left(x\right)$ and interpret it.

(e)

To determine

Calculate $\sigma$.

(f)

To determine

Compute the exact probability that x is in the interval $\mu \pm 2\sigma$.

Compare the answer with Chebyshev’s rule and interpret the result.