**Problem Statement:** Assume that the random variable X is normally distributed, with mean \( \mu = 40 \) and standard deviation \( \sigma = 8 \). Compute the probability \( P(X < 50) \). **Choices:** - A) 0.8944 - B) 0.9015 - C) 0.1056 - D) 0.8849 **Explanation:** To solve this problem, use the properties of the normal distribution. Convert the score of 50 to a z-score using the formula: \[ z = \frac{X - \mu}{\sigma} \] With \( X = 50 \), \( \mu = 40 \), and \( \sigma = 8 \): \[ z = \frac{50 - 40}{8} = \frac{10}{8} = 1.25 \] Once the z-score is found, use a standard normal distribution table or calculator to find \( P(Z < 1.25) \). The value you locate will be the probability that a value is less than 50 in this distribution. Compare the result to the choices given.
**Problem Statement:** Assume that the random variable X is normally distributed, with mean \( \mu = 40 \) and standard deviation \( \sigma = 8 \). Compute the probability \( P(X < 50) \). **Choices:** - A) 0.8944 - B) 0.9015 - C) 0.1056 - D) 0.8849 **Explanation:** To solve this problem, use the properties of the normal distribution. Convert the score of 50 to a z-score using the formula: \[ z = \frac{X - \mu}{\sigma} \] With \( X = 50 \), \( \mu = 40 \), and \( \sigma = 8 \): \[ z = \frac{50 - 40}{8} = \frac{10}{8} = 1.25 \] Once the z-score is found, use a standard normal distribution table or calculator to find \( P(Z < 1.25) \). The value you locate will be the probability that a value is less than 50 in this distribution. Compare the result to the choices given.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Problem Statement:**
Assume that the random variable X is normally distributed, with mean \( \mu = 40 \) and standard deviation \( \sigma = 8 \). Compute the probability \( P(X < 50) \).
**Choices:**
- A) 0.8944
- B) 0.9015
- C) 0.1056
- D) 0.8849
**Explanation:**
To solve this problem, use the properties of the normal distribution. Convert the score of 50 to a z-score using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
With \( X = 50 \), \( \mu = 40 \), and \( \sigma = 8 \):
\[ z = \frac{50 - 40}{8} = \frac{10}{8} = 1.25 \]
Once the z-score is found, use a standard normal distribution table or calculator to find \( P(Z < 1.25) \).
The value you locate will be the probability that a value is less than 50 in this distribution. Compare the result to the choices given.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d4c8cb-af63-459c-8cdf-c777fdfe530a%2Fb0ecbb34-4f04-45d6-a8be-e3d8c031b486%2Fuczt94c.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Assume that the random variable X is normally distributed, with mean \( \mu = 40 \) and standard deviation \( \sigma = 8 \). Compute the probability \( P(X < 50) \).
**Choices:**
- A) 0.8944
- B) 0.9015
- C) 0.1056
- D) 0.8849
**Explanation:**
To solve this problem, use the properties of the normal distribution. Convert the score of 50 to a z-score using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
With \( X = 50 \), \( \mu = 40 \), and \( \sigma = 8 \):
\[ z = \frac{50 - 40}{8} = \frac{10}{8} = 1.25 \]
Once the z-score is found, use a standard normal distribution table or calculator to find \( P(Z < 1.25) \).
The value you locate will be the probability that a value is less than 50 in this distribution. Compare the result to the choices given.
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