Question

A pollster asked 100 people “If money was not a factor, how many children would you like to have?” The results and their frequencies are shown in the (estimated) probability distribution function table below.

X - P(X)
0 - .25
1 - .26
2 - .29
3 - .15
4 - .05

What is the probability that the number of children a randomly selected person from this sample would like to have is less than the mean of X?

Answer 1

(C) 0.51

Step-by-step explanation:

The missing probability, P(X = 0) = 1 – 0.26 – 0.29 – 0.15 – 0.05 = 0.25.

\mu _{x}μ x = (0)(0.25) + (1)(0.26) + (2)(0.29) + (3)(0.15) + (4)(0.05) = 1.49 children.

P(X < 1.49) = P(X = 0 or X = 1) = 0.25 + 0.26 = 0.51.