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d. What is the probability that a randomly selected watermelon will weigh more than 6.5 kg? e. What is the probability that a randomly selected seedless watermelon will weigh between 6.7 and 7.7 kg? f. The 80th percentile for the weight of seedless watermelons is kg.

d. What is the probability that a randomly selected watermelon will weigh more than 6.5 kg? e. What is the probability that a randomly selected seedless watermelon will weigh between 6.7 and 7.7 kg? f. The 80th percentile for the weight of seedless watermelons is kg.

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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please answer d. e. and f.

### Normal Distribution of Seedless Watermelon Weights Suppose that the weight of seedless watermelons is normally distributed with a mean of 6.1 kg and a standard deviation of 1.5 kg. Let \( X \) be the weight of a randomly selected seedless watermelon. Round all answers to four decimal places where possible. #### Questions: a. **What is the distribution of \( X \)?** \( X \sim N(\text{mean}, \text{standard deviation}) \) b. **What is the median seedless watermelon weight?** ____ kg c. **What is the Z-score for a seedless watermelon weighing 6.6 kg?** ____ d. **What is the probability that a randomly selected watermelon will weigh more than 5.5 kg?** ____ e. **What is the probability that a randomly selected seedless watermelon will weigh between 6.7 and 7.7 kg?** ____ f. **The 80th percentile for the weight of seedless watermelons is** ____ kg #### Explanation of Key Concepts: - **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable. This distribution is symmetric and characterized by its mean (average) and standard deviation. - **Z-score:** Represents the number of standard deviations a data point is from the mean. It is a way of standardizing scores across different scales. - **Percentiles:** A measure used in statistics indicating the value below which a given percentage of observations fall. For example, the 80th percentile is the value below which 80% of the data points lie.
Transcribed Image Text:### Normal Distribution of Seedless Watermelon Weights Suppose that the weight of seedless watermelons is normally distributed with a mean of 6.1 kg and a standard deviation of 1.5 kg. Let \( X \) be the weight of a randomly selected seedless watermelon. Round all answers to four decimal places where possible. #### Questions: a. **What is the distribution of \( X \)?** \( X \sim N(\text{mean}, \text{standard deviation}) \) b. **What is the median seedless watermelon weight?** ____ kg c. **What is the Z-score for a seedless watermelon weighing 6.6 kg?** ____ d. **What is the probability that a randomly selected watermelon will weigh more than 5.5 kg?** ____ e. **What is the probability that a randomly selected seedless watermelon will weigh between 6.7 and 7.7 kg?** ____ f. **The 80th percentile for the weight of seedless watermelons is** ____ kg #### Explanation of Key Concepts: - **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable. This distribution is symmetric and characterized by its mean (average) and standard deviation. - **Z-score:** Represents the number of standard deviations a data point is from the mean. It is a way of standardizing scores across different scales. - **Percentiles:** A measure used in statistics indicating the value below which a given percentage of observations fall. For example, the 80th percentile is the value below which 80% of the data points lie.
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