Let X1, X2, ... X100 be 100 independent and identically distributed continuous random variables with mean = 37 and variance = 25. Let S = X1 + X2 + ... + X100, Use the Central Limit Theorem to...

Let X1, X2, ... X100 be 100 independent and identically distributed continuous random<br>variables with mean<br>= 37 and variance<br>= 25.<br>Let S = X1 + X2 + ... + X100, Use the Central Limit Theorem to approximate the probability<br>that S is less than 3800 i.e. P(S<3800). Enter your answer to 4 decimal places.<br>Hint: Calculate the mean<br>and variance<br>of S. By the Central Limit Theorem, S is approximately normally distributed with mean<br>and variance<br>when the sample size is larger than 30. In other words, standardization of S leads to<br>S- Hs<br>

Extracted text: Let X1, X2, ... X100 be 100 independent and identically distributed continuous random variables with mean = 37 and variance = 25. Let S = X1 + X2 + ... + X100, Use the Central Limit Theorem to approximate the probability that S is less than 3800 i.e. P(S<3800). enter="" your="" answer="" to="" 4="" decimal="" places.="" hint:="" calculate="" the="" mean="" and="" variance="" of="" s.="" by="" the="" central="" limit="" theorem,="" s="" is="" approximately="" normally="" distributed="" with="" mean="" and="" variance="" when="" the="" sample="" size="" is="" larger="" than="" 30.="" in="" other="" words,="" standardization="" of="" s="" leads="" to="" s-="">

Jun 11, 2022

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Let X1, X2, ... X100 be 100 independent and identically distributed continuous random variables with mean = 37 and variance = 25. Let S = X1 + X2 + ... + X100, Use the Central Limit Theorem to...

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