ind standard deviatio
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!
Find standard deviations.
![High school students across the nation compete in a financial capability
challenge each year by taking a National Financial Capability Challenge
Exam. Students who score in the top 21 percent are recognized publicly
for their achievement by the Department of the Treasury. Assuming a
normal distribution, how many standard deviations above the mean
does a student have to score to be publicly recognized? (Round your
answer to 2 decimal places.)
Standard deviations](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5ce7534-59ca-460f-b63d-1de5b1ebd643%2Fac771811-c8ba-482f-8e06-97f8cbc5a6f1%2Fxnfsrsp_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Provided data is,
High school students across the nation compete in a financial capability challenge each year by taking a national financial capacity challenge exam. Students who score in top 21% are recognized publicly for their achievement by the department of treasury assuming a normal distribution.
If random variable X~N(µ, σ2), then
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