Questions: 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. 0.0948 C. 0.4920 D. 0.4910

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. 0.0948 C. 0.4920 D. 0.4910
Transcript text: 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. 0.0948 C. 0.4920 D. 0.4910
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Solution

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Solution Steps

Step 1: Identify the Z-scores

The Z-score for a is -2.41 and for b is 0.

Step 2: Use the Standard Normal Distribution Table

Using the Z-table, we find $P(Z \leq a)$ is approximately 0.008 and $P(Z \leq b)$ is approximately 0.5.

Step 3: Calculate the Desired Probability

The probability that $Z$ lies between -2.41 and 0 is $P(a < Z < b) = P(Z \leq b) - P(Z \leq a) = 0.5 - 0.008 = 0.492$.

Final Answer: The probability that $Z$ lies between -2.41 and 0 is approximately 0.492.

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