The average amount of money that people spend at Don Mcalds fast food place is $7.4400 with a standard deviation of $1.5400. 6 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. The average amount of money that people spend at Don Mcalds fast food place is $7.4400 with a standarddeviation of $1.5400. 6 customers are randomly selected. Please answer the following questions, and roundall answers to 4 decimal places where possible and assume a normal distribution.a. What is the distribution of X? X - N(b. What is the distribution of î? ¤ - N(c. What is the distribution of > x? >aΣd. What is the probability that one randomly selected customer will spend less than $7.3170?e. For the 6 customers, find the probability that their average spent is less than $7.317o.f. Find the probability that the randomly selected 6 customers will spend less than $43.9020.g. For part e) and f), is the assumption of normal necessary? O NoO Yesh. The owner of Don Mcalds gives a coupon for a free sundae to the 5% of all groups of 6 people whospend the most money. At least how much must a group of 6 spend in total to get the free sundae? $

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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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The average amount of money that people spend at Don Mcalds fast food place is $7.4400 with a standard deviation of $1.5400. 6 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Given:

$\begin{array}{rcl} μ & = & 7.4400 \\ σ & = & 1.5400 \\ n & = & 6 \end{array}$

a) The distribution of X is X~N $(μ, σ^{2})$ .

Thus, the distribution of X is X~N $(7.4400, 1 . 5400^{2})$ .

b) The distribution of sample $\bar{x}$ , $\bar{x}$ ~N $(μ, \frac{σ}{\sqrt{n}})$ .

Thus, the distribution of $\bar{x}$ is $\bar{x}$ ~N $(7.4400, \frac{1.5400}{\sqrt{n}})$

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