According to researchers, the mean length of imprisonment for motor-vehicle-theft offenders in a nation is 16.7 months. One hundred randomly selected motor-vehicle-theft offenders in a city in the nation had a mean length of imprisonment of 17.9 months. At the 1% significance level, do the data provide sufficient evidence to conclude that the mean length of imprisonment for motor-vehicle-theft offenders in the city differs from the national mean? Assume that the population standard deviation of the lengths of imprisonment for motor-vehicle-theft offenders in the city is 8.0 months. Set up the hypotheses for the one-mean z-test. Ho: H VO Ha: V (Type integers or decimals. Do not round.) The test statistic is z = (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) V the mean length of imprisonment for the null hypothesis. The data motor-vehicle-theft offenders in the nation. sufficient evidence to conclude that the mean length of imprisonment for motor-vehicle-theft offenders in the city is

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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!