Given that z is a standard normal random variable, compute the following probabilities. P(-1.23 < z < 2.41)Question 8Select one:a.0.9920b.0.8827c.0.8872d.0.1093
Question
Given that z is a standard normal random variable, compute the following probabilities. P(-1.23 < z < 2.41)Question 8Select one:a.0.9920b.0.8827c.0.8872d.0.1093
Solution
To solve this problem, we need to find the area under the standard normal curve between -1.23 and 2.41.
Step 1: Look up the z-scores in the z-table (also known as the standard normal table).
The z-table gives us the probability that a standard normal random variable is less than a given value.
Step 2: Find the probabilities corresponding to the z-scores -1.23 and 2.41.
From the z-table, P(Z < -1.23) = 0.1093 and P(Z < 2.41) = 0.9920.
Step 3: Subtract the probabilities to find the probability that Z is between -1.23 and 2.41.
P(-1.23 < Z < 2.41) = P(Z < 2.41) - P(Z < -1.23) = 0.9920 - 0.1093 = 0.8827.
So, the correct answer is b. 0.8827.
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