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Riana Miren and Trinh are 40 and 57 years old, respectively. Based on a normal distribution with mean 49.3 years and standard deviation 11.8, what is the probability that a skydiver will be between 40 and 57 years of age? 0.5277 0.2702 0.9455 0.0545

Riana Miren and Trinh are 40 and 57 years old, respectively. Based on a normal distribution with mean 49.3 years and standard deviation 11.8, what is the probability that a skydiver will be between 40 and 57 years of age? 0.5277 0.2702 0.9455 0.0545

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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**Probability in Normal Distribution: Age Range of Skydivers** **Question:** Riana Miren and Trinh are 40 and 57 years old, respectively. Based on a normal distribution with a mean of 49.3 years and a standard deviation of 11.8, what is the probability that a skydiver will be between 40 and 57 years of age? **Options:** - 0.5277 - 0.2702 - 0.9455 - 0.0545 In this problem, we are to find the probability that a skydiver falls within the given age range. It is important to reference the properties of the normal distribution to determine this probability, using the provided mean and standard deviation. **Solution Steps:** 1. Convert age limits (40 and 57 years) into z-scores using the z-score formula: \( z = \frac{(x - \mu)}{\sigma} \), where \( x \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. 2. Use the z-scores to find the corresponding probabilities from the standard normal distribution table. 3. Subtract the smaller probability from the larger probability to find the probability that a skydiver will be between 40 and 57 years of age. Review the multiple-choice options to find the correct probability associated with the calculated value.
Transcribed Image Text:**Probability in Normal Distribution: Age Range of Skydivers** **Question:** Riana Miren and Trinh are 40 and 57 years old, respectively. Based on a normal distribution with a mean of 49.3 years and a standard deviation of 11.8, what is the probability that a skydiver will be between 40 and 57 years of age? **Options:** - 0.5277 - 0.2702 - 0.9455 - 0.0545 In this problem, we are to find the probability that a skydiver falls within the given age range. It is important to reference the properties of the normal distribution to determine this probability, using the provided mean and standard deviation. **Solution Steps:** 1. Convert age limits (40 and 57 years) into z-scores using the z-score formula: \( z = \frac{(x - \mu)}{\sigma} \), where \( x \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. 2. Use the z-scores to find the corresponding probabilities from the standard normal distribution table. 3. Subtract the smaller probability from the larger probability to find the probability that a skydiver will be between 40 and 57 years of age. Review the multiple-choice options to find the correct probability associated with the calculated value.
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