Question

Given tGiven the following probability distribution, find P (X = 3).

Answer 1

1.) P(X = 3) = 1 - (0.4 + 0.1 + 0.15 + 0.2) = 1 - 0.85 = 0.15

2a.) To verify that the probability is legimate, we sum it and see if the sum is 1. 0.09 + 0.36 + 0.35 + 0.13 + 0.05 + 0.02 = 1
Since the sum of the probabilities is 1, the probability is a legitimate probability distribution.
b.) P(x > 2) is the probability that the number of cars an American family owns is greater than 2.
c.) P(x = 2) is the probability that the number of cars an American family owns is 2.
d.) P(x > 2) => P(x = 3) + P(x = 4) + P(x = 5) = 0.13 + 0.05 + 0.02 = 0.2

3a.) The percent of the sons that reached the highest class is 0.01 x 100% = 1%
b.) 0.48 + 0.38 + 0.08 + 0.05 + 0.01 = 1
Since the sum of the probabilities is 1, the distribution meets the requirements of a discrete probability distribution.
c.) P(x < 2) = P(x = 1) = 0.48
d.) P(x = 2) = 0.38