D thru F only The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 6 ounces. 35 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.a. What is the distribution of $X$? $X \sim N(\underline{\hspace{3em}}, \underline{\hspace{3em}})$b. What is the distribution of $\bar{x}$? $\bar{x} \sim N(\underline{\hspace{3em}}, \underline{\hspace{3em}})$c. What is the probability that one randomly selected person drinks between 15.7 and 16.1 ounces of coffee per day? $\underline{\hspace{3em}}$d. For the 35 people, find the probability that the average coffee consumption is between 15.7 and 16.1 ounces of coffee per day. $\underline{\hspace{3em}}$e. For part d), is the assumption that the distribution is normal necessary? $\square$ No $\square$ Yesf. Find the IQR for the average of 35 coffee drinkers.Q1 = $\underline{\hspace{3em}}$ ouncesQ3 = $\underline{\hspace{3em}}$ ouncesIQR: $\underline{\hspace{3em}}$ ounces

Answered: D thru F only

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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D thru F only

The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 6 ounces. 35 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

a. What is the distribution of $X$? $X \sim N(\underline{\hspace{3em}}, \underline{\hspace{3em}})$

b. What is the distribution of $\bar{x}$? $\bar{x} \sim N(\underline{\hspace{3em}}, \underline{\hspace{3em}})$

c. What is the probability that one randomly selected person drinks between 15.7 and 16.1 ounces of coffee per day? $\underline{\hspace{3em}}$

d. For the 35 people, find the probability that the average coffee consumption is between 15.7 and 16.1 ounces of coffee per day. $\underline{\hspace{3em}}$

e. For part d), is the assumption that the distribution is normal necessary?

$\square$ No $\square$ Yes

f. Find the IQR for the average of 35 coffee drinkers.

Q1 = $\underline{\hspace{3em}}$ ounces

Q3 = $\underline{\hspace{3em}}$ ounces

IQR: $\underline{\hspace{3em}}$ ounces

Expert Solution

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A z-score represents the position of a data point in terms of its distance from the mean when measured in standard deviation units, i.e, how far the observation is from the mean in units of standard deviation.

The z of a variable (x) is the ratio of the difference of mean $μ$ from the data point (x) by the standard deviation $σ$ , i.e, $z = \frac{x - μ}{σ}$

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