The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. Find the probability that a randomly selected person with a kidney stone will take longer than 14 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.

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Please answer A, B, & C please. Thank you in advance!!! Help is appreciated :) 

**Educational Material on Kidney Stone Passage Time**

The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let \( X \) = time to pass the kidney stone. Round all answers to 4 decimal places where possible.

**Questions:**

a. What is the distribution of \( X \)?
\[ X \sim N(\boxed{16}, \boxed{6^2}) \]

b. Find the probability that a randomly selected person with a kidney stone will take longer than 14 days to pass it.
\[ P(X > 14) = \boxed{\quad} \]

c. Find the minimum number for the upper quarter of the time to pass a kidney stone.
\[ x = \boxed{\quad} \text{ days} \]

**Note:** 

- In question (a), the distribution of \( X \) is written in the form \( N(\mu, \sigma^2) \), where \( \mu \) is the mean and \( \sigma^2 \) is the variance.
- Questions (b) and (c) are referring to probabilities and percentiles, which involve calculations using the normal distribution parameters provided.
- There are no graphs or diagrams included in the provided image. If required, normal distribution curve visualizations may help in understanding these concepts better.
Transcribed Image Text:**Educational Material on Kidney Stone Passage Time** The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let \( X \) = time to pass the kidney stone. Round all answers to 4 decimal places where possible. **Questions:** a. What is the distribution of \( X \)? \[ X \sim N(\boxed{16}, \boxed{6^2}) \] b. Find the probability that a randomly selected person with a kidney stone will take longer than 14 days to pass it. \[ P(X > 14) = \boxed{\quad} \] c. Find the minimum number for the upper quarter of the time to pass a kidney stone. \[ x = \boxed{\quad} \text{ days} \] **Note:** - In question (a), the distribution of \( X \) is written in the form \( N(\mu, \sigma^2) \), where \( \mu \) is the mean and \( \sigma^2 \) is the variance. - Questions (b) and (c) are referring to probabilities and percentiles, which involve calculations using the normal distribution parameters provided. - There are no graphs or diagrams included in the provided image. If required, normal distribution curve visualizations may help in understanding these concepts better.
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