In this paper, some properties of the arithmetic and harmonic means of the length-biased distribution are utilized for the Inverse Gaussian distribution (IGD). These result in interesting applications of the inverse moments and give useful modified asymptotic tests for certain parameters of the original IGD based on the sample taken from the corresponding length-biased IGD. In particular, asymptotic tests and confidence intervals are presented for the mean and the coefficient of variation of the IGD. An example is provided to illustrate the procedure. Finally, an estimator of the reliability function based on the length biased data is derived and its efficiency is examined.