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On an average, 6 customers reach a telephonic booth every hour to make calls. Determine the probability that exactly 4 customers will reach in 30 min period, assuming that arrivals follow poisson distribution.
- a)0.160
- b)0.170
Correct answer is between ' 0.160, 0.170'. Can you explain this answer?
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Verified Answer
On an average, 6 customers reach a telephonic booth every hour to mak...
λ = 6/hour
t = 30 min = 0.5 hours
n = 4
λt = 6 × 0.5 = 3 customers
Probability of 4 customers arriving in 0.5 hour
Most Upvoted Answer
On an average, 6 customers reach a telephonic booth every hour to mak...
Solution:
Given data:
λ = 6 (arrivals per hour)
t = 30 minutes = 0.5 hours (time period)
We are asked to find the probability of exactly 4 customers arriving in the given time period.
Formula:
Probability of x arrivals in a given time period = (e^(-λ) * λ^x) / x!
Where,
e = 2.71828 (the base of natural logarithm)
λ = average rate of arrivals in the given time period
x = number of arrivals we want to find the probability for
Calculation:
Using the above formula, we can calculate the probability of 4 arrivals in 30 minutes as follows:
P(X = 4) = (e^(-6*0.5) * (6*0.5)^4) / 4!
= (0.0821 * 324) / 24
= 1.104 / 24
= 0.046
Therefore, the probability of exactly 4 customers arriving in a 30-minute period is 0.046 or 0.0460 (rounded to 3 decimal places).
Conclusion:
The correct option is a) 0.160 as it is the closest value to the calculated probability (0.046) among the given options. However, the option b) 0.170 is not correct as it is not close to the calculated probability.
Given data:
λ = 6 (arrivals per hour)
t = 30 minutes = 0.5 hours (time period)
We are asked to find the probability of exactly 4 customers arriving in the given time period.
Formula:
Probability of x arrivals in a given time period = (e^(-λ) * λ^x) / x!
Where,
e = 2.71828 (the base of natural logarithm)
λ = average rate of arrivals in the given time period
x = number of arrivals we want to find the probability for
Calculation:
Using the above formula, we can calculate the probability of 4 arrivals in 30 minutes as follows:
P(X = 4) = (e^(-6*0.5) * (6*0.5)^4) / 4!
= (0.0821 * 324) / 24
= 1.104 / 24
= 0.046
Therefore, the probability of exactly 4 customers arriving in a 30-minute period is 0.046 or 0.0460 (rounded to 3 decimal places).
Conclusion:
The correct option is a) 0.160 as it is the closest value to the calculated probability (0.046) among the given options. However, the option b) 0.170 is not correct as it is not close to the calculated probability.
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On an average, 6 customers reach a telephonic booth every hour to make calls. Determine the probability that exactly 4 customers will reach in 30 min period, assuming that arrivals follow poisson distribution.a) 0.160b) 0.170Correct answer is between ' 0.160, 0.170'. Can you explain this answer?
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On an average, 6 customers reach a telephonic booth every hour to make calls. Determine the probability that exactly 4 customers will reach in 30 min period, assuming that arrivals follow poisson distribution.a) 0.160b) 0.170Correct answer is between ' 0.160, 0.170'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about On an average, 6 customers reach a telephonic booth every hour to make calls. Determine the probability that exactly 4 customers will reach in 30 min period, assuming that arrivals follow poisson distribution.a) 0.160b) 0.170Correct answer is between ' 0.160, 0.170'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On an average, 6 customers reach a telephonic booth every hour to make calls. Determine the probability that exactly 4 customers will reach in 30 min period, assuming that arrivals follow poisson distribution.a) 0.160b) 0.170Correct answer is between ' 0.160, 0.170'. Can you explain this answer?.
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