The table below shows the probability distribution of students in a high school with 1500 students. What is the expected value for the age of a randomly chosen student?
Age
13, 14, 15, 16, 18
Probability
0.01, 0.28, 0.30, 0.25,0.15,0.01
A. 15.28
B. 15.64
C. 15.34
D. 15.36
Answers
Answer: 15.28
Step-by-step explanation:
The expected value for the age of a randomly chosen student is,
⇒ 15.28
Given that:
Total number of students,
⇒ n = 1500,
And, Age : 13, 14, 15, 16, 17, 18
Probability : 0.01, 0.25, 0.27, 0.30, 0.16, 0.01
Now,
We can Calculate the expected value as shown below,
E = 13 × 0.01 + 14 × 0.25 + 15 × 0.27 + 16 × 0.30 + 17 × 0.16 + 18 × 0.01
E = 0.13 + 3.5 + 4.05 + 4.8 + 2. 72 + 0.18
E = 15.38
Therefore, The expected value for the age of a randomly chosen student is 15.38.
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