The average height of a woman aged 20-74 years is 162,5cm. Suppose that the height is normally distributed with a standard deviation 5cm. (a) what is the probability a randomly selected woman in this population is between 155 and 175 centimeters? (b) Determine the height that is symmetric about the mean and includes 90% of population? (c) What is the probability that five women chosen randomly all exceed 172cm?
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 average height of a woman aged 20-74 years is 162,5cm. Suppose that the height is
-
(a) what is the probability a randomly selected woman in this population is between 155 and 175 centimeters?
-
(b) Determine the height that is symmetric about the mean and includes 90% of population?
-
(c) What is the probability that five women chosen randomly all exceed 172cm?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
