a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean…

a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean of the probability distribution below? probability distribution

Answer

Explanation:

Step1: Identify values and probabilities

Let (x_1 = 1), (P(x_1)=0.1); (x_2 = 2), (P(x_2)=0.2); (x_3 = 3), (P(x_3)=0.4); (x_4 = 4), (P(x_4)=0.2); (x_5 = 5), (P(x_5)=0.1).

Step2: Use mean formula for discrete - random variables

The mean (\mu=\sum_{i = 1}^{n}x_iP(x_i)), so (\mu=1\times0.1 + 2\times0.2+3\times0.4 + 4\times0.2+5\times0.1).

Step3: Calculate each product

(1\times0.1=0.1), (2\times0.2 = 0.4), (3\times0.4=1.2), (4\times0.2 = 0.8), (5\times0.1=0.5).

Step4: Sum up the products

(\mu=0.1 + 0.4+1.2 + 0.8+0.5=3).