Questior The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service one customer every six minutes. Cars arrive at the regular unleaded pump at an average of 6 customers per hour. a) What is the average time a customer waits in the queue to receive service? b) Management of Petroco likes to have its operators working 90% of the time. What must the arrival rate be for the pump attendant to be as busy as management would like? c) The average waiting time computed in (a) above is not pleasant to management and it wishes to reduce it. There are two alternatives open to management. First, management can add an assistant to the attendant and this will improve the service rate to one customer every four minutes. This assistant will receive a salary of GHC100 per month. The second alternative is that management can add a second pump which will cost GHC2,000 and this amount is a free gift from Suobogbiree & Sons. This alternative will reduce the arrival rate to 3 every hour however, Petroco will have to pay the attendant a monthly salary of GHC150. Whichever alternative management adopts, Petroco avoids a lost sale of GH¢100 for every minute that average waiting time is reduced. Could you advise management which alternative it must adopt?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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