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Using a standard normal distribution, find the following probabilities. Round your answers to three decimal places. P(Z < 2.53) P(Z > 1) = = P(-2.28 < Z < 0.61)

Using a standard normal distribution, find the following probabilities. Round your answers to three decimal places. P(Z < 2.53) P(Z > 1) = = P(-2.28 < Z < 0.61)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Standard Normal Distribution: Probability Calculations** When dealing with a standard normal distribution, you can find specific probabilities for given z-values. Below are three tasks to help you practice. 1. **Probability Calculation for Z less than 2.53:** \[ P(Z < 2.53) = \_\_\_ \] Calculate the probability that a standard normal variable is less than 2.53 and round your answer to three decimal places. 2. **Probability Calculation for Z greater than 1:** \[ P(Z > 1) = \_\_\_ \] Compute the probability that a standard normal variable is greater than 1. Make sure to round your answer to three decimal places. 3. **Probability Calculation for Z between -2.28 and -0.61:** \[ P(-2.28 < Z < -0.61) = \_\_\_ \] Determine the probability that the standard normal variable falls between -2.28 and -0.61. Round the answer to three decimal places. Use a standard normal distribution table or statistical software to find these probabilities accurately.
Transcribed Image Text:**Understanding Standard Normal Distribution: Probability Calculations** When dealing with a standard normal distribution, you can find specific probabilities for given z-values. Below are three tasks to help you practice. 1. **Probability Calculation for Z less than 2.53:** \[ P(Z < 2.53) = \_\_\_ \] Calculate the probability that a standard normal variable is less than 2.53 and round your answer to three decimal places. 2. **Probability Calculation for Z greater than 1:** \[ P(Z > 1) = \_\_\_ \] Compute the probability that a standard normal variable is greater than 1. Make sure to round your answer to three decimal places. 3. **Probability Calculation for Z between -2.28 and -0.61:** \[ P(-2.28 < Z < -0.61) = \_\_\_ \] Determine the probability that the standard normal variable falls between -2.28 and -0.61. Round the answer to three decimal places. Use a standard normal distribution table or statistical software to find these probabilities accurately.
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Step 1

Answer: - Given, A standard normal distribution

                Find the following probabilities

                (a) P(Z < 2.53) =

                (b) P(Z > 1) =

               (c) P(-2.28 < Z < -0.61) =

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