Johnson Filtration, Inc. provides maintenance service for water-filtration systems. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow. Click on the datafile logo to reference the data. DATA file Repair Time Months Since in Hours Last Service Type of Repair Repairperson 2.9 Electrical Dave Newton 3.0 6. Mechanical Dave Newton 4.8 8. Electrical Bob Jones 1.8 3. Mechanical Dave Newton 2.9 Electrical Dave Newton 4.9 Electrical Bob Jones 4.2 6. Mechanical Bob Jones 4.8 8. Mechanical Bob Jones 4.4 4 Electrical Bob Jones 4.5 6. Electrical Dave Newton a. Ignore for now the months since the last maintenance service (æ1 ) and the repairperson who performed the service. Develop the estimated simpe linear regression equation to predict the repair time (y) given the type of repair (2 ). Recall that a2 0 if the type of repair is mechanical and 1 if the type of repair is electrical (to 2 decimals). Time = Туpe b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (to 4 decimals) No because the p-value of shows that the relationship is not significant for any reasonable value of a.
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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