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Soft-drink dispenser. The manager of a local soft-drink
Chapter 4, Problem 147E(choose chapter or problem)
Problem 147E
Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beveragedispensing machine is set to dispense 7 ounces, it in fact dispenses an amount x at random anywhere between 6.5 and 7.5 ounces inclusive. Suppose x has a uniform probability distribution.
a. Is the amount dispensed by the beverage machine a discrete or a continuous random variable? Explain.
b. Graph the frequency function for x, the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.
c. Find the mean and standard deviation for the distribution graphed in part b and locate the mean and the interval on the graph.
d. Find
e. Find
f. Find
g. What is the probability that each of the next six bottles filled by the new machine will contain more than 7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.
Questions & Answers
QUESTION:
Problem 147E
Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beveragedispensing machine is set to dispense 7 ounces, it in fact dispenses an amount x at random anywhere between 6.5 and 7.5 ounces inclusive. Suppose x has a uniform probability distribution.
a. Is the amount dispensed by the beverage machine a discrete or a continuous random variable? Explain.
b. Graph the frequency function for x, the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.
c. Find the mean and standard deviation for the distribution graphed in part b and locate the mean and the interval on the graph.
d. Find
e. Find
f. Find
g. What is the probability that each of the next six bottles filled by the new machine will contain more than 7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.
ANSWER:
Solution:
Step 1 of 3:
The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces.
An amount x at random anywhere between 6.5 and 7.5 ounces inclusive.
Here x has a uniform probability distribution.
We have to find,
- Is the amount dispensed by the beverage machine a discrete or a continuous random variable.
- We have to draw the graph of the frequency function for x.
-
The mean and standard deviation for the distribution graphed in part b and we have to locate the mean and the interval
on the graph.
-
P(x
.
- P(x<6).
-
P(6.5
.
- The probability that each of the next six bottles filled by the new machine will contain more than 7.25 ounces of beverage.