Problem
If $z$ is a standard normal variable, find the probability that $z$ lies between -2.41 and 0. Round to four decimal places. A. 0.5080 B. 0.4920 C. 0.0948 D. 0.4910
Solution
Step 1 ：Let $z$ be a standard normal variable, which follows a normal distribution with mean 0 and standard deviation 1.
Step 2 ：We are asked to find the probability that $z$ lies between -2.41 and 0.
Step 3 ：This probability is the cumulative distribution function (CDF) at 0 minus the CDF at -2.41.
Step 4 ：The CDF at 0 is 0.5 and the CDF at -2.41 is 0.007976260260733725.
Step 5 ：Subtract the CDF at -2.41 from the CDF at 0 to find the probability that $z$ lies between -2.41 and 0.
Step 6 ：\(0.5 - 0.007976260260733725 = 0.4920237397392663\)
Step 7 ：Round this probability to four decimal places to get the final answer.
Step 8 ：Final Answer: The probability that $z$ lies between -2.41 and 0 is \(\boxed{0.4920}\).
