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.)

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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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