Question

a physics professor wants to know what percent of physics majors will spend the next two years doing post - graduate research. he has the following probability distribution.

x	p(x)	x*p(x)
1	0.35
2	0.20
3	0.15

|4|

5	0.10
6	0.05

find the probability that a physics major will do post - graduate research for at most three years. p(x ≤ 3) =

a. 0.20 + 0.15+0.05 + 0.40

b. 0.35 + 0.20+0.15 = 0.70

c. 0.10 + 0.05 = 0.15

Explanation:

Step1: Identify the required probability

We need to find $P(x\leq3)$. This means we sum the probabilities for $x = 1$, $x=2$ and $x = 3$.

Step2: Sum the relevant probabilities

$P(x\leq3)=P(1)+P(2)+P(3)$. Given $P(1) = 0.35$, $P(2)=0.20$ and $P(3)=0.15$. So $P(x\leq3)=0.35 + 0.20+0.15$.

Step3: Calculate the sum

$0.35+0.20 + 0.15=0.70$

Answer:

$0.70$