A Portfolio consists of six investment products. The expected return of each investment, in million GPB$,$ is normally distributed as follows: Investment I ~ N$(70,16)$; Investment II ~ N$(42,25)$; Investment III ~ N$(60,4)$; Investment IV ~ N$(20,4)$; Investment V ~ N$(18,16)$; Investment VI ~ N$(28,4)$; The returns from the six investments are independent.

I. Find the distribution of the total Portfolio return. Report the mean, the variance and the standard deviation.

II$.$ If the total return exceeds $251$ million GPB$,$ a bonus will be given. What is the probability that this bonus will be given?

III. If the total return is less than $218$ million GPB$,$ the client will look for other firms to handle his money in the future. What is the probability that the firm will keep this customer?