According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. Find the probability that the person is between 62.3 and 65.5 inches. c. The middle 50% of Martian heights lie between what two numbers? Low: inches High: inches
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. Find the probability that the person is between 62.3 and 65.5 inches. c. The middle 50% of Martian heights lie between what two numbers? Low: inches High: inches
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Title: Analyzing the Heights of Martian Adult Males**
According to a study conducted by UCB students, the heights of Martian adult males follow a normal distribution. The mean height is 64 inches, with a standard deviation of 2.5 inches. Suppose we randomly choose one Martian adult male and define \(X\) as the height of this individual. All answers should be rounded to four decimal places.
**a. Distribution of Height for Martian Adult Males**
- The variable \(X\) is normally distributed, denoted as:
\[
X \sim N(\, \_ , \_ \,)
\]
where the blanks are to be filled with the mean and standard deviation.
**b. Probability Calculation**
- Calculate the probability that the height of a Martian adult male lies between 62.3 inches and 65.5 inches. Fill in the provided blank with the probability value.
**c. Interquartile Range of Heights**
- Determine the range that contains the middle 50% of Martian heights.
- **Low:** \(\_\_\_\_\_\_\_\) inches
- **High:** \(\_\_\_\_\_\_\_\) inches
**Hint:** Use the properties of the normal distribution to find these values.
This exercise involves understanding normal distributions, calculating probabilities, and determining interquartile ranges within a given dataset.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d201130-f4f7-4c89-8a7d-8eb0f7158013%2F62b1b304-bee9-41f3-a74d-a80be6e5fdcd%2Fwazrx89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing the Heights of Martian Adult Males**
According to a study conducted by UCB students, the heights of Martian adult males follow a normal distribution. The mean height is 64 inches, with a standard deviation of 2.5 inches. Suppose we randomly choose one Martian adult male and define \(X\) as the height of this individual. All answers should be rounded to four decimal places.
**a. Distribution of Height for Martian Adult Males**
- The variable \(X\) is normally distributed, denoted as:
\[
X \sim N(\, \_ , \_ \,)
\]
where the blanks are to be filled with the mean and standard deviation.
**b. Probability Calculation**
- Calculate the probability that the height of a Martian adult male lies between 62.3 inches and 65.5 inches. Fill in the provided blank with the probability value.
**c. Interquartile Range of Heights**
- Determine the range that contains the middle 50% of Martian heights.
- **Low:** \(\_\_\_\_\_\_\_\) inches
- **High:** \(\_\_\_\_\_\_\_\) inches
**Hint:** Use the properties of the normal distribution to find these values.
This exercise involves understanding normal distributions, calculating probabilities, and determining interquartile ranges within a given dataset.
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