1. Dental disease in domestic cats is commonly associated with the accumulation of plaque on the teeth. A cat food manufacturer is studying the accumulation of plaque on the teeth of cats from a certain population. The accumulation of plaque is assessed using a fluorescent light technique (FLT), where an evaluator reviews images of the cat's teeth and assigns an overall rating from 0 to 100, with lower values indicating less plaque. A previous study indicates the population distribution of the FLT ratings for the teeth of cats is bimodal with mean u = 59 and standard deviation o = 20 (a) Compare the shapes of the sampling distributions of the sample mean FLT rating for random samples of 3 cats and for random samples of 60 cats from the population. Explain your answer. (b) Which of the following would be more likely to obtain from the population? A random sample of 100 cats having a mean FLT rating that is less than 54 or A random sample of 400 cats having a mean FLT rating that is less than 54 Justify your answer.
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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