Question Tag: Expected Value

(i) Expected Value (E(X)):
The expected value is calculated as follows:

E (X) =

E (X) = (0×0.10) + (1×0.30) + (2×0.40) + (3×0.12) + (4×0.06) + (5×0.02)

E (X) = 0 + 0.30 + 0.80 + 0.36 + 0.24 + 0.10 = 1.80

Thus, the expected value of the number of cars per household is 1.80.

(ii) Standard Deviation (σ):
First, calculate the variance:

Var (X) =

       Var (X) = 0.324+0.192+0.016+0.173+0.290+0.205=1.20

Now, calculate the standard deviation:

Thus, the standard deviation is 1.095.

iii)

Relative Percentage Histogram:

(iv) Comments on the Distribution:
The distribution of car ownership is positively skewed, as the expected value (1.80) is closer to the lower end of the range, and most households own 1 or 2 cars. The data shows that only a small percentage of households own more than 3 cars, contributing to the positive skewness.