Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. For the 18 people, find the probability that the average age that they learned to walk is between 11.5 and 13.5 months old. For part d), is the assumption that the distribution is normal necessary? NoYes
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 the age that children learn to walk is
- For the 18 people, find the
probability that the average age that they learned to walk is between 11.5 and 13.5 months old. - For part d), is the assumption that the distribution is normal necessary? NoYes
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