In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About 68% of people who are murdered actually knew the person who committed the murder.† Suppose that a detective file in New Orleans has 67 current unsolved murders. Find the following probabilities. (Round your answers to four decimal places.) (a) at least 35 of the victims knew their murderers (b) at most 48 of the victims knew their murderers (c) fewer than 30 victims did not know their murderers (d) more than 20 victims did not know their murderers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the
What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About 68% of people who are murdered actually knew the person who committed the murder.† Suppose that a detective file in New Orleans has 67 current unsolved murders. Find the following probabilities. (Round your answers to four decimal places.)
(b) at most 48 of the victims knew their murderers
(c) fewer than 30 victims did not know their murderers
(d) more than 20 victims did not know their murderers
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