23. In an automatic telephone exchange the probability that anyone call is wrongly connected is 0.001. What is the minimum number of independent calls required to ensure a probability of 0.90, that at least one call is wrongly connected? Fit a Poisson distribution to the set of observations: x 0 1 2 3 4 f 122 60 15 2 1
Added by Mar-A J.
Close
Step 1
We are given that $p = 0.001$. Let $n$ be the number of independent calls. We want to find the minimum $n$ such that the probability of at least one call being wrongly connected is at least 0.90. The probability that at least one call is wrongly connected is given Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N 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
The telephone exchange inside an office building has a number of outside lines of which, on average, 3 are being used at any instant. Assuming that the number of lines in use at any instant follows a Poisson distribution. Applying the Poisson model, evaluate the minimum number of outside lines required if there is a probability of more than 0.9 that, at any given instant, at least one of the lines is not being used.
Supreeta N.
In a telephone exchange, the probability of any one call being wrongly connected is 0.003. For a day when 1800 calls are connected, determine the probability that at MOST 2 wrong connections are made. Use the Poisson distribution to find the approximate value of the probability asked for in part (a). What is the minimum number of calls required to ensure a probability of 0.8 that at least one call is wrongly connected? Suppose the owner receives an income of 10p for each connection but loses £15 for each wrong connection. What is the average profit per day with 1800 calls?
Lien L.
The telephone exchange inside an office building has a number of outside lines of which, on average, 3 are being used at any instant. Assuming that the number if lines in use at any instant follows a Poisson distribution. Applying the Poisson model, evaluate the minimum number of outside lines required if there is a probability of more than 0.9 that, at any given instant, at least one of the lines is not being used.
Madhur L.
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