A set of distinct numbers is normally distributed with mean m and standard deviation s, where 0<s<m. If a random number from the set is duplicated and inserted into the set, what is the probability that the new mean is greater than m?

I think , not very sure the ans is 1/2 , this is how I did it.

Suppose the set is a1,a2,a3,a4,a5 then mean would be a3 and to make the mean greater we will duplicate numbers above the mean that is if we see in a normal distribution would comprise of 32+14+2 (approximately ) = 50 and the total is 100 , therefore 50/100=1/2.

Not sure though, please correct me if my approach is wrong.

Hey Mansi,

Answer is 1/2 only

thank you for your help