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

It appears that I am unable to directly calculate the probabilities using the tools available. Instead, I will provide the calculations manually using standard normal distribution tables or a calculator. ### Step 1: Calculate \( P(Z > 2.19) \) 1. **Find \( P(Z \leq 2.19) \)**: - Using a standard normal distribution table or calculator, we find: \[ P(Z \leq 2.19) \approx 0.9857 \] 2. **Calculate \( P(Z > 2.19) \)**: \[ P(Z > 2.19) = 1 - P(Z \leq 2.19) = 1 - 0.9857 = 0.0143 \] ### Step 2: Calculate \( P(-2.35 < Z < 2.1) \) 1. **Find \( P(Z < 2.1) \)**: - Using a standard normal distribution table or calculator, we find: \[ P(Z < 2.1) \approx 0.9821 \] 2. **Find \( P(Z \leq -2.35) \)**: - Using a standard normal distribution table or calculator, we find: \[ P(Z \leq -2.35) \approx 0.0094 \] 3. **Calculate \( P(-2.35 < Z < 2.1) \)**: \[ P(-2.35 < Z < 2.1) = P(Z < 2.1) - P(Z \leq -2.35) = 0.9821 - 0.0094 = 0.9727 \] ### Final Answers 1. \( P(Z > 2.19) \approx 0.0143 \) 2. \( P(-2.35 < Z < 2.1) \approx 0.9727 \) Thus, the probabilities are: - \( P(Z > 2.19) = 0.0143 \) - \( P(-2.35 < Z < 2.1) = 0.9727 \)