Question

Following is the probability distribution for the age of a student at a certain public high school. х 13 14 15 16 17 18 P(x) 0.08 0.24 0.23 0.28 0.14 0.03 a. Find the expected value of the ages. (2 decimal places) b. Find the standard deviation of the ages. (4 decimal places) c. Find the probability that the age of a randomly selected student is 18. d. Would it be unusual for the age of a randomly selected student to be 18? Check

Answer 1

16 17 18 Total Solution:- We have given probability distribution of X as X 13 14 15 P(X) 0.08 0.24 0.23 X*P(X) 1.04 3.36 3.45 X^2*P(x) 13.52 47.04 51.75 0.03 1 0.28 4.48 71.68 0.14 2.38 40.46 0.54 9.72 15.25 234.17 a) Find expected value of X by definition of expected value, it is given by E(X) = Sum[X*P(x)] E(X) = 15.25 from above table b) Find standard deviation of X by definition of standard deviation, it is given by Sd(x) = sqrt{ E(X^2) - (E(X))^2 } but E(X^2) = Sum(x^2*P(x)) E(X^2) = 234.17 -----from above table therefore, Sd(x) = sqrt { 234.17 -(15.25)^2} Sd(X) =Sqrt { 1.6075 Sd(X) = 1.2679 c) find probability that age of randomly selected student is 18 ------> from above table P(X=18) = 0.03 therefore, The probability that the age of randomly selected student is 18 = 0.03 d) Would it be unusual for the age of randomly selected student to be 18? Yes, Because, the probability that the age of randomly selected student to be 18 is 0.03 and this probability 0.03 is less than 0.05