Final answer:
The probability mass function (PMF) of C, the cost of a telephone call, is P(C = $0.20) = 0.6 for voice calls and P(C = $0.30) = 0.4 for data calls. Other probabilities closely linked to this concept are calculated using Poisson distribution formulas for the given mean rates.
Step-by-step explanation:
The question involves finding the probability mass function (PMF) of the cost of a telephone call. Voice calls cost 20 cents each, and data calls cost 30 cents each. The probability of a call being a voice call is P[V] = 0.6, and the probability of a data call is P[D] = 0.4. The random variable C can take on two values: $0.20 for voice calls and $0.30 for data calls. Hence, the PMF of C is:
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- P(C = $0.20) = P[V] = 0.6
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- P(C = $0.30) = P[D] = 0.4
Small companies monitoring telephone call costs could find this statistical assessment helpful for managing expenses.
To address the reference information:
a. The average time between calls is 15 seconds (0.25 minutes).
c. If the number of calls per minute follows a Poisson distribution with a mean of four calls per minute, the probability of exactly five calls occurring within a minute is:
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- P(X = 5) = (4^5 * e^-4) / 5!
e. To find the probability that fewer than 20 calls occur within an hour:
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- P(X < 20) can be calculated using the Poisson distribution formula with the appropriate mean for one hour.