The number of machine failures per month in a certain plant has a Poisson distribution with mean equal to 3. a) Find the probability that on a given month, at least one machine fails in the plant. Give your answer to three decimal places. b) Find the cost (in thousands of dollars) to the plant of machine failures can be approximated as: X = 12+7*Y+ Y^2 Find (to one decimal place) the expected cost of machine failures per month (in thousands of dollars).
Added by Nicole H.
Step 1
The Poisson distribution formula is: P(Y=k) = (e^(-λ) * λ^k) / k! where Y is the number of failures, k is the number of occurrences, and λ is the mean (3 in this case). So, the probability of no machine failures (k=0) is: P(Y=0) = (e^(-3) * 3^0) / 0! = Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 99 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the probability that there will be no machine breakdown in a particular month. (On average there are 18 machine breakdowns in a year. Assume that the number of machine breakdowns in a month follows the Poisson Distribution.) A) 0.22 B) 0.33 C) 0.42 D) 0.52
Aman G.
1. The number of machine breakdown, per day at a factory follows the Poisson distribution. Based on a random observation during 30 days, it was found that the number of machine breakdown was 2.5 machines / day. Please answer the following question: a) Please calculate the expected value of machine breakdown for the period of: i. One day ii. Two days iii. Three days. b) What is the probability of having 2 machine breakdowns in two days period? c) What is the probability of having more than 2 machine breakdowns in one day period? d) What is the probability of having 2 machine breakdowns in the first day and 1 machine breakdown in the second day, for two consecutive days? e) If the loss of each machine breakdown is IDR 1 million, what is the expected value of the loss from machine breakdown per day?
Ameer S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD