15.2.32 One dimensional random variables and their characteristics

Problem: Random errors in measuring the distance to the fixed target are subject to the normal law of distribution with the expected value of \( a=5 \mathrm{~m} \) and the dispersion \( \sigma^{2}=100 \mathrm{~m}^{2} \). Determine the probability that: a) the measured value of the distance deviates from the true value by more than \( 15 \mathrm{~m} \). b) for three independent measurement the error of at least one measurement will not exceed \( 15 \mathrm{~m} \) in the absolute value.