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The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 7 mL. Suppose that 15 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of x? a - N( c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 61.8 mL.

The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 7 mL. Suppose that 15 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of x? a - N( c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 61.8 mL.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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The content explores a statistical problem involving the amount of syrup people use on their pancakes, which follows a normal distribution with a mean of 59 mL and a standard deviation of 7 mL. The context involves observing 15 randomly selected individuals for their syrup usage. Answers are to be rounded to four decimal places. a. **Distribution of \( X \):** - \( X \sim N(\_\_\_\_\_\) b. **Distribution of \( \overline{x} \):** - \( \overline{x} \sim N(\_\_\_\_\_\) c. **Probability for a Single Individual:** - Probability that a randomly selected individual consumes between 60.1 mL and 61.8 mL: \( \_\_\_\_\_ \) d. **Probability for 15 Individuals:** - Probability that the average amount is between 60.1 mL and 61.8 mL for the group of 15: \( \_\_\_\_\_ \) e. **Normal Distribution Assumption:** - Is assuming the distribution is normal necessary for part d)? - No [ ] - Yes [ ] This structured outline provides a step-by-step guide to solving a normal distribution and probability problem, which is useful in teaching students about sampling distributions and hypothesis testing in statistics.
Transcribed Image Text:The content explores a statistical problem involving the amount of syrup people use on their pancakes, which follows a normal distribution with a mean of 59 mL and a standard deviation of 7 mL. The context involves observing 15 randomly selected individuals for their syrup usage. Answers are to be rounded to four decimal places. a. **Distribution of \( X \):** - \( X \sim N(\_\_\_\_\_\) b. **Distribution of \( \overline{x} \):** - \( \overline{x} \sim N(\_\_\_\_\_\) c. **Probability for a Single Individual:** - Probability that a randomly selected individual consumes between 60.1 mL and 61.8 mL: \( \_\_\_\_\_ \) d. **Probability for 15 Individuals:** - Probability that the average amount is between 60.1 mL and 61.8 mL for the group of 15: \( \_\_\_\_\_ \) e. **Normal Distribution Assumption:** - Is assuming the distribution is normal necessary for part d)? - No [ ] - Yes [ ] This structured outline provides a step-by-step guide to solving a normal distribution and probability problem, which is useful in teaching students about sampling distributions and hypothesis testing in statistics.
Expert Solution
Step 1

(a)

Determine the distribution of X.

The distribution of X is obtained below as follows:

Statistics homework question answer, step 1, image 1

 

 

Step 2

(b)

Statistics homework question answer, step 2, image 1

Thus, the value of sample mean of the sampling distribution is 59.

 

The value of the sampling distribution of the standard deviation is,

 

Statistics homework question answer, step 2, image 2

 

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