Consider the standard normal distribution and find \( \mathrm{P}(-1.56<\mathrm{Z}<0.22) \). 00.4723 00.5277 00.4129 00.0594 00.5871

To find the probability \( \mathrm{P}(-1.56<\mathrm{Z}<0.22) \) for a standard normal distribution, you can use a standard normal distribution table or calculator. 1. Find \( \Phi(0.22) \): This gives you the probability that Z is less than 0.22. You'll find that \( \Phi(0.22) \approx 0.5871 \). 2. Find \( \Phi(-1.56) \): This gives you the probability that Z is less than -1.56. You'll find that \( \Phi(-1.56) \approx 0.0594 \). Now, calculate the difference: \[ \mathrm{P}(-1.56 < Z < 0.22) = \Phi(0.22) - \Phi(-1.56) \approx 0.5871 - 0.0594 = 0.5277 \] So the probability \( \mathrm{P}(-1.56<\mathrm{Z}<0.22) \) is approximately \( \text{00.5277} \). To summarize: 00.5277