An article in Electronic Journal of Applied Statistical Analysis [“Survival Analysis of Acute Myocardial Infarction Patients Using Non-Parametric and Parametric Approaches” (2009, Vol. 2(1), pp. 22–36)] described the use of a Weibull distribution to model the survival time of acute myocardial infarction (AMI) patients in a hospital-based retrospective study. The shape and scale parameters for the Weibull distribution in the model were 1.16 and 0.25 years, respectively. Determine the following:

(a) Mean and standard deviation of survival time

(b) Probability that a patient survives more than a year

(c) Survival time exceeded with probability 0.9