Read the scenarios below. For each data set, decide if you believe they would follow a normal distribution. Explain your reasoning and why you made that decision. The hand span (measured from the tip of the thumb to the tip of the extended 5th finger) of a random sample of high school seniors. The annual salaries of all employees of a large shipping company. The annual salaries of a random sample of 50 CEOs of major companies, 25 women and 25 men. The dates of 100 pennies taken from a cash drawer in a convenience store. Then think of your own example of a data set that would follow a normal distribution and explain why.
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!
Read the scenarios below. For each data set, decide if you believe they would follow a
- The hand span (measured from the tip of the thumb to the tip of the extended 5th finger) of a random sample of high school seniors.
- The annual salaries of all employees of a large shipping company.
- The annual salaries of a random sample of 50 CEOs of major companies, 25 women and 25 men.
- The dates of 100 pennies taken from a cash drawer in a convenience store.
Then think of your own example of a data set that would follow a normal distribution and explain why.
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