Question

A random variable X has a mean value of 5 and variance of 3.

(i) What is the least value of ( | − 5| < 3)
(ii) What value of ‘h’ guarantees that P( |X − 5| < ℎ) ≥ 0.99

(iii) What is the least value of P( |X − 5| < 7.5)​

Answer 1

Answer:

(I) 0.667

(ii) h= 17.32

(iii) 0.946

Answer 2

Step-by-step explanation:

(I)The least value of ( |x − 5| < 3)  0.667

by taking the function out of modulus.

(ii) The value of ‘h’ that guarantees P( |X − 5| < ℎ) ≥ 0.99 is h= 17.32

(iii) The least value of P( |X − 5| < 7.5)​ is 0.946