Question 3 Calculate the probability for the following problems (Please keep 4 decimal places). 1. \( P(\mathrm{Z}>2.19)= \) 3. \( P(-2.35<2.1)= \)

To find \( P(Z > 2.19) \), you would typically look up the value in a standard normal distribution table or use a calculator that provides cumulative probabilities. The cumulative probability \( P(Z \leq 2.19) \) is approximately 0.9857. Therefore, \( P(Z > 2.19) = 1 - P(Z \leq 2.19) = 1 - 0.9857 = 0.0143 \). For \( P(-2.35 < Z < 2.1) \), you find \( P(Z < 2.1) \) and \( P(Z < -2.35) \). From the standard normal table, \( P(Z < 2.1) \) is about 0.9821 and \( P(Z < -2.35) \) is approximately 0.0094. Thus, \( P(-2.35 < Z < 2.1) = P(Z < 2.1) - P(Z < -2.35) = 0.9821 - 0.0094 = 0.9727 \).