The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 20.5 foot tall?
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!
The
a. What is the distribution of X? X ~ N(,)
b. What is the
c. What is the Z-score for a giraffe that is 20.5 foot tall?
d. What is the probability that a randomly selected giraffe will be shorter than 19.9 feet tall?
e. What is the probability that a randomly selected giraffe will be between 18.9 and 19.8 feet tall?
f. The 80th percentile for the height of giraffes is ft.
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