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Suppose X~Bin(100, ¹). (a) Compute the exact value for P(X ≤ 90). (Hint: you need to use the pbinom () function in R) (b) If you use a normal distribution to approximate the binomial distribution, what would the normal distribution be? That is, you need to figure out the mean and variance of the normal distribution. (Hint: recall the formulas for the expected value and variance of a binomial random variable.) (c) Using the normal distribution you obtained part (b), estimate P(X < 90). (Hint: you need to use the pnorm () function in R.)

Suppose X~Bin(100, ¹). (a) Compute the exact value for P(X ≤ 90). (Hint: you need to use the pbinom () function in R) (b) If you use a normal distribution to approximate the binomial distribution, what would the normal distribution be? That is, you need to figure out the mean and variance of the normal distribution. (Hint: recall the formulas for the expected value and variance of a binomial random variable.) (c) Using the normal distribution you obtained part (b), estimate P(X < 90). (Hint: you need to use the pnorm () function in R.)

MATLAB: An Introduction with Applications
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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Suppose X~ Bin (100, ¹). (a) Compute the exact value for P(X<90). (Hint: you need to use the pbinom () function in R) (b) If you use a normal distribution to approximate the binomial distribution, what would the normal distribution be? That is, you need to figure out the mean and variance of the normal distribution. (Hint: recall the formulas for the expected value and variance of a binomial random variable.) (c) Using the normal distribution you obtained part (b), estimate P(X < 90). (Hint: you need to use the pnorm () function in R.) (d) Are your answers for parts (a) and (c) similar?
Transcribed Image Text:Suppose X~ Bin (100, ¹). (a) Compute the exact value for P(X<90). (Hint: you need to use the pbinom () function in R) (b) If you use a normal distribution to approximate the binomial distribution, what would the normal distribution be? That is, you need to figure out the mean and variance of the normal distribution. (Hint: recall the formulas for the expected value and variance of a binomial random variable.) (c) Using the normal distribution you obtained part (b), estimate P(X < 90). (Hint: you need to use the pnorm () function in R.) (d) Are your answers for parts (a) and (c) similar?
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