Estimating normal distribution from samples in a range

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I have an event whose result I conjecture is distributed normally. I have taken many hundreds, even thousands of samples of this event, and noted every result below a certain value (1 minute) - 123 results. I'm wondering if it's possible to use just this lower range of the assumed normal distribution to estimate the mean and variance? Or even, if the theory that the results come from a normal distribution can be tested despite only recording biased samples?