TransUnion is a leading global provider of business intelligence services. Transunion reported that 33% of the mortgages in the year previous to the sub-prime mortgage crisis were adjustable-rate mortgages (ARMs). a. In samples of mortgages of size 75, what proportion of the samples would you expect to produce sample proportions equal to or larger than 0.25? b. If a sample of size 75 produced a sample proportion of 0.45, what would you infer that the population proportion of mortgages with ARMs really is? c. In a sample of 90 mortgages, what would the probability be that the number of mortgages with ARMS would be between 25 and 35?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
TransUnion is a leading global provider of business intelligence services. Transunion reported that 33% of the mortgages in the year previous to the sub-prime mortgage crisis were adjustable-rate mortgages (ARMs).
- a. In samples of mortgages of size 75, what proportion of the samples would you expect to produce sample proportions equal to or larger than 0.25?
- b. If a
sample of size 75 produced a sample proportion of 0.45, what would you infer that the population proportion of mortgages with ARMs really is? - c. In a sample of 90 mortgages, what would the
probability be that the number of mortgages with ARMS would be between 25 and 35?
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