Questions: Question 2 (1 point) Find P(1.31<Z<2.15). Round answer to 4 decimal places. Answer: A)

Transcript text: Question 2 (1 point) Find $P(1.31

Solution

Solution Steps

To find the probability $ P(1.31 < Z < 2.15) $, we need to use the standard normal distribution table or a computational tool to find the cumulative probabilities for $ Z = 1.31 $ and $ Z = 2.15 $. The probability $ P(1.31 < Z < 2.15) $ is the difference between these two cumulative probabilities.

Step 1: Determine Cumulative Probabilities

To find $ P(1.31 < Z < 2.15) $, we first determine the cumulative probabilities for $ Z = 1.31 $ and $ Z = 2.15 $ using the standard normal distribution. The cumulative probability for $ Z = 2.15 $ is approximately 0.9842, and for $ Z = 1.31 $ it is approximately 0.9049.

Step 2: Calculate the Probability of the Range

The probability $ P(1.31 < Z < 2.15) $ is the difference between the cumulative probabilities for $ Z = 2.15 $ and $ Z = 1.31 $. Therefore, we calculate: \[ P(1.31 < Z < 2.15) = 0.9842 - 0.9049 = 0.0793 \]

Final Answer

The probability $ P(1.31 < Z < 2.15) $ is $\boxed{0.0793}$.

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