1) Describe what an unusual event is. What is the typical cutoff point for unusu
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1) Describe what an unusual event is. What is the typical cutoff point for unusual events? 2) Are mutually exclusive events always independent? Give one example to support the answer. Are independent events always mutually exclusive? Give one example to support the answer. 3) If 25 people are randomly selected, find the probability that no 2 of them have the same birthday (Ugnore leap years). Explain your answer. 4) Explain what "success" means in a binomial probability. List 4 requirements of a binomial probability distribution. 5) Explain how the value of p, the probability of success, affects the shape of the binomial probability histogram. Explain how the value of n, the number of trials in a binomial experiment, affects the shape of the binomial probability histogram. 6) What is the difference between a standard normal distribution and a nonstandard normal distribution? 7) Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.Explanation / Answer
1) An unusual event is an event that has a low probability of occurring. Typically, we say that an event with a probability less than 5% is unusual. So cutoff point is probability =0.05
2) Two events are said to be mutually exclusive if they cannot occur both at the same instance and two events are said to be independent if occurrence of one does not effect the occurrence of the other event.
Two mutually exclusive events are not necessarily independent. As in case of tossing of coin, getting head or tail are two mutually exclusive events but they are not independent. As if head occur tail cannot occur and vice versa.
Two independent events are not necessarily mutually exclusive. For example
If two coins are tossed. The event that the first coin comes up head is independent from the event that the second comes up head. But the two events are not mutually exclusive as it can happen that both coins show heads
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