A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of u ounces per cup. If the ounces of soda dispensed are normally distributed with standard deviation 0.5 ounces, find a value of u such that 36-ounce cups will overflow only 10% of the time. Round the solution to one decimal place, if necessary. ounces
A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of u ounces per cup. If the ounces of soda dispensed are normally distributed with standard deviation 0.5 ounces, find a value of u such that 36-ounce cups will overflow only 10% of the time. Round the solution to one decimal place, if necessary. ounces
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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![**Problem Statement:**
A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of \( \mu \) ounces per cup. If the ounces of soda dispensed are normally distributed with a standard deviation of 0.5 ounces, find a value of \( \mu \) such that 36-ounce cups will overflow only 10% of the time. Round the solution to one decimal place, if necessary.
**Solution:**
The goal is to determine the average \( \mu \) such that the probability of dispensing more than 36 ounces is only 10%. Using the properties of the normal distribution, we'll find the z-score that corresponds to the top 10% of the distribution and use it to solve for \( \mu \).
\[ \mu = \, \_\_\_ \, \text{ounces} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec7d0b78-7026-4f2e-9cd3-9f6affde891c%2F92ddffb1-8afa-4386-9d45-3013e94187f2%2F7le36xr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of \( \mu \) ounces per cup. If the ounces of soda dispensed are normally distributed with a standard deviation of 0.5 ounces, find a value of \( \mu \) such that 36-ounce cups will overflow only 10% of the time. Round the solution to one decimal place, if necessary.
**Solution:**
The goal is to determine the average \( \mu \) such that the probability of dispensing more than 36 ounces is only 10%. Using the properties of the normal distribution, we'll find the z-score that corresponds to the top 10% of the distribution and use it to solve for \( \mu \).
\[ \mu = \, \_\_\_ \, \text{ounces} \]
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