Get the answer to "Rock noise in an underground mine occurs at..."

High School
Statistics and Probability
High school statistics
Data distributions

Ann Tice

Answered question

2021-11-28

Rock noise in an underground mine occurs at an average rate of three per hour. Find the probability that no rock noise will be recorded for at least 30 minutes.

Answer & Explanation

Mary Moen

Beginner2021-11-29Added 14 answers

Step 1
From the information, the number of rock noises occurs on the average 3 per every hour. That is,

λ = 3

. Here, the time period is 30 minutes, That is,

w = \frac{1}{2}

.
Let X denotes the number of rock noise occur on the 30 minutes period. Hence X follows Poisson with parameter

λ w

.
Step 2
The probability that no rock noise will be recorded for at least 30 minutes is 0.2231, which is obtained below:

P (X = x) = \frac{e^{- λ w} λ w^{x}}{x!}

P (X = 0) = \frac{e^{- 3 (\frac{1}{2}) {(3 (\frac{1}{2}))}^{0}}}{0!}

= \frac{e^{- 1.5} {1.5}^{0}}{0!}

= 0.2231

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