Question

The probabilities that a building inspector will observe 0, 1, 2, 3, 4, or 5 code violations in a newly constructed suburban home are 0.48, 0.25, 0.14, 0.08, 0.04, and 0.01, respectively. What are the mean and standard deviation of building code violations?

Answer 1

The probability distribution is

X=       0    1   2        3        4        5
P(X)= 0.48   0.25   0.14   0.08   0.04   0.01

The mean of the given distribution, we will use the following formula:

$\mu=\sum X*P(X)$

$\mu=0.98$

Standard deviation is calculated as

Now,

Finnaly