The Johnson family uses a propane gas grill for cooking outdoors. During the sum
ID: 2784332 • Letter: T
Question
The Johnson family uses a propane gas grill for cooking outdoors. During the summer they need to replace their tank on average every 24 days. At a randomly chosen moment, determine the following:
What is the probability that they can grill out at least 34 days before they need to replace their tank? (Round your answer to 4 decimal places.)
What is the probability that they can grill out no more than 10 days? (Round your answer to 4 decimal places.)
The Johnson family uses a propane gas grill for cooking outdoors. During the summer they need to replace their tank on average every 24 days. At a randomly chosen moment, determine the following:
Explanation / Answer
a. 24.17%
Average number of replacements = 34/24 = 1.42
Using the Poisson formula
P = [e^(-a)](a^x)/x!
where x= actual number of replacements which is zero in this case
Hence P= e^-1.42 * 1.42^0
=2.718^-1.42 * 1 = 24.17%
b. 65.91%
Average = 10/24 = 0.417
Using the Poisson formula
P = [e^(-a)](a^x)/x!
where x= actual number of replacements which is zero in this case
Hence P= e^- 0.417 * 0.417^0
P= 2.718^ -0.417 * 1
= 65.91%
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