MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Suppose you roll a fair, 4-sided die once every day for 360 days.
[Image source: https://commons.wikimedia.org/wiki/File:4-sided_dice_250.jpg (Links to an external site.) ; Author: Fantasy; CC BY-SA 3.0 (Links to an external site.)]
Let X represent the number of rolls that land with "1" at the bottom edge of the die, as in the illustration above. Note: the
- X is a binomial random variable. What are the parameters n and p for its distribution?
- Without evaluating the expression, use the binomial formula to write out exactly P(X = 81). You should not evaluate the binomial coefficient, nor the exponential expressions. Do not give a decimal approximation; use Formula 5.1 from our textbook (Section 5.3).
- We want to use the normal approximation to the binomial to approximate the probability P(85 < X ≤ 95).
- Check that normal approximation is reasonable in this case. (This is Step 2 of Procedure 6.3, p. 299 in our textbook.)
- What are the mean and standard deviation of the appropriate
normal distribution? (Step 3 of Procedure 6.3.) - What is the correction for continuity to evaluate this probability? I.e., what are the endpoints a and b so that, if Y denotes the normal random variable, we have
P(85 < X ≤ 95) ≈ P(a ≤ Y ≤ b) ? - Find the probability given by the approximation. If possible, also find the exact value of P(85 < X ≤ 95), using technology. How does the approximation compare to the exact value?
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