A consumer-research company selects several models of cars each year to study fuel efficiency. This year, they want to examine two car brands in their work. Based on the independent and randomly obtained samples from two normally distributed populations, it is desired to test whether the B brand car has a higher average fuel consumption. (a=0.05) Brand A Brand B sample width 12 Sample mean (miles) 27.2 32.1 Mass standard deviation 3.8 4.3 Which of the following is true for the relevant hypothesis and test statistic? O A. Ho:H1 – H2 = 0 , H1: µ1 – µz > 0 ,z=2.9 O B. Ho: H1 – Hz = 0 . H1: µ1 – Hz > 0, t=3.5 O C. Ho:H1 – µz = 0, H1: µ1 – µz < 0. t=-2.5 D. Ho:H1 – H2 = 0 , H1: µ1 – µz < 0, z=-2.72

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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!