Answer to Question #340119 in Statistics and Probability for Maneo

Question

In a sample of 500 families, 95 have an annual income of less than M80 000, 272 families have an annual salary of M80 000 to M150 000 and the remaining families have an annual income of more than M150 000. One family is randomly selected from these 500 families. Find the probability that this family has an annual income of:

• A) less than M80 000

• B) more than M150 000

• C) M80 000 to M150 000 or more than M150 000

• D) Show that the probability of the sample space is equal to 1

Answer 1

A)

$$P(X<M80000)=\dfrac{95}{500}=0.190$$

B)

$$P(X>M150000)=\dfrac{500-95-272}{500}=0.266$$

C)

$$P(M80000\le X\le M150000\cup X>M150000)$$

$$=\dfrac{272+(500-95-272)}{500}=0.810$$

D)

$$P(S)=P(X<M80000)$$

$$+P(M80000\le X\le M150000)$$

$$+P( X>M150000)$$

$$=0.190+\dfrac{272}{500}+0.266=1$$