This thesis is concerned with estimating the probability that at least k out of n random variables $X_1,X_2,\ldots,X_n$ are smaller than a random variable Y. It is assumed that $X_1,X_2,\ldots,X_n$ have two parameters exponential distribution and Y has normal distribution, and that they are all independent. Maximum likelihood estimator, minimum variance unbiased estimator of the probability are obtained. For conjugate prior distributions of the parameters and the squared error loss, Bayes estimator is also obtained. Performance of the three estimators for moderate sample sizes is studied by Monte Carlo simulation and a numerical example is given.
