Mean or Expected Value and Standard Deviation · Exercise 9

A physics professor wants to know what percent of physics majors will spend the next several years doing postgraduate research. He has the following probability distribution:
$$\begin{array}{ccc}\text{x}& \text{P(x)}& \text{x*P(x)}\\ \text{1}& \text{.35}& \\ \text{2}& \text{.20}& \\ \text{3}& \text{.15}& \\ \text{4}& & \\ \text{5}& \text{.10}& \\ \text{6}& \text{.05}& \end{array}$$

Find the probability that a physics major will do postgraduate research for at most three years. P(x ≤ 3) = ________

This exercise has fill-in blanks from its source book and no answer key.

OpenStax, Statistics · §4.2 Mean or Expected Value and Standard Deviation · Exercise 9