In each of the following situations, which of the two distributions would be more spread out? Standard normal distribution or t-distribution with df = 10. t-distribution with df = 5 or t-distribution with df = 25. t-distribution with df = 100 or normal distribution with standard deviation = 100.
Konciljev56
Answered question
2022-09-14
Answer & Explanation
Adrienne Harper
Beginner2022-09-15Added 14 answers
a) Any student t-distribution is wider than the normal distribution, but it is especially wider for t-distributions with df=10.
b) The t-distribution with df=5 is wider because the spread widens as the number of degrees of freedom increases.
c) If you keep in mind that the Student tt-distribution with df=100 is roughly equivalent to the standard normal random variable and that its standard deviation is 1, you'll realize that the differences between the two distributions are hardly perceptible. Specially, this means that they have about the same spread.
However, increasing the normal distribution's standard deviation to 100 will cause it to have very high spread, much greater than the standard deviation being 1.
From the above we can conclude that normal distribution with standard deviation of 100 is (much) more spread out.
Result:
a) t-distribution; b) t-distribution with df=5; c) Normal distribution
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