Heights of a Group of 19th-Century Boys, Age 14 Height (in inches) Percent of boys Under 50 0.2 50-54 7.0 55-59 46.0 60-64 41.0 65-69 5.8 SOURCE: Journal of the Anthropological Institute of Great Britain and Ireland
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!
Boys’ Heights Humans are, on average, taller ‘today than they were 200 years ago. Today, the mean height of 14-year-old boys is about 65 in. Use the following relative frequency distribution of heights of a group of 14-year-old boys from the 19th century to answer the following questions
a. What percent of the group of 19th-century boys was at least 65 in. tall?
b. What is the probability that one of the 19th-century boys selected at random was at least 55 in. tall hut less than 65 in. tall?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
