Below is a distribution of race in the United States from 2014. White= 60.5% Black= 12.5% Hispanic= 18.3% Asian= 5.7% Other= 3% If we were to randomly choose 150 people for a survey, what is the probability that less than 70 of them would be white (round to 3 decimal places)? Would this be unusual? If so, give some reasons why a particular sample might have less than 70 whites. What is the probability that we would randomly choose a sample of 150 people and more than 22 of them were black (to 3 decimal places)? What is the probability you would randomly select two Americans and they would both be white? How many Asian people should we expect to have in a randomly selected group of 150 people?
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!
- Below is a distribution of race in the United States from 2014.
White= 60.5%
Black= 12.5%
Hispanic= 18.3%
Asian= 5.7%
Other= 3%
If we were to randomly choose 150 people for a survey, what is the probability that less than 70 of them would be white (round to 3 decimal places)?
Would this be unusual? If so, give some reasons why a particular sample might have less than 70 whites.
What is the probability that we would randomly choose a sample of 150 people and more than 22 of them were black (to 3 decimal places)?
What is the probability you would randomly select two Americans and they would both be white?
How many Asian people should we expect to have in a randomly selected group of 150 people?
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