It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with 374 minutes and standard deviation 64 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 522 minutes and standard deviation 104 minutes. A researcher records the minutes of activity for an SRS of 5 mildly obese people and an SRS of 5 lean people. (a) What is the probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 400 minutes? (Enter your answer rounded to four decimal places.)
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!
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