Suppose that the mean value of the interpupillary distance for all adult males is 65 mm, and the population standard deviation is 5 mm. If the distribution of interpupillary distance is normal and a sample of n=25 adult males is selected, what is the probability that the same average distance, x-bar, for these 25 scores will be between 64 and 67 mm? Same set-up as part a. More than 68 mm? Suppose that a sample of 100 adult males is obtained. Without assuming that interpupillary distance is normally distributed, what is the approximate probability that the average distance, x-bar, is between 64 and 67 mm? Same set-up as part c. More than 68 mm?
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!
Suppose that the
- If the distribution of interpupillary distance is normal and a sample of n=25 adult males is selected, what is the
probability that the same average distance, x-bar, for these 25 scores will be between 64 and 67 mm? - Same set-up as part a. More than 68 mm?
- Suppose that a sample of 100 adult males is obtained. Without assuming that interpupillary distance is
normally distributed , what is the approximate probability that the average distance, x-bar, is between 64 and 67 mm? - Same set-up as part c. More than 68 mm?
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