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

Answer

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Answer

Final Answer: The probability that $z$ lies between -2.41 and 0 is \(\boxed{0.4920}\).

Steps

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 \(\boxed{0.4920}\).

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