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 vhen the sample size is larger than 30. In other words, standardization of S leads to S- Hs
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 vhen the sample size is larger than 30. In other words, standardization of S leads to S- Hs
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
![Let \( X_1, X_2, \ldots, X_{100} \) be 100 independent and identically distributed continuous random variables with mean
\[
\mu
\]
= 37 and variance
\[
\sigma^2
\]
= 25.
Let \( S = X_1 + X_2 + \ldots + X_{100} \). Use the Central Limit Theorem to approximate the probability that \( S \) is less than 3800, i.e., \(\text{P}(S < 3800)\). Enter your answer to 4 decimal places.
**Hint:** Calculate the mean
\[
\mu_S
\]
and variance
\[
\sigma^2_S
\]
of \( S \). By the Central Limit Theorem, \( S \) is approximately normally distributed with mean
\[
\mu_S
\]
and variance
\[
\sigma^2_S
\]
when the sample size is larger than 30. In other words, standardization of \( S \) leads to
\[
\frac{S - \mu_S}{\sigma_S} \approx Z
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8b48535-184f-4977-af2d-d816dbce40fd%2Fa80c1f14-4cdb-4fda-9ff6-7e058b69d956%2Fc1t9znr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( X_1, X_2, \ldots, X_{100} \) be 100 independent and identically distributed continuous random variables with mean
\[
\mu
\]
= 37 and variance
\[
\sigma^2
\]
= 25.
Let \( S = X_1 + X_2 + \ldots + X_{100} \). Use the Central Limit Theorem to approximate the probability that \( S \) is less than 3800, i.e., \(\text{P}(S < 3800)\). Enter your answer to 4 decimal places.
**Hint:** Calculate the mean
\[
\mu_S
\]
and variance
\[
\sigma^2_S
\]
of \( S \). By the Central Limit Theorem, \( S \) is approximately normally distributed with mean
\[
\mu_S
\]
and variance
\[
\sigma^2_S
\]
when the sample size is larger than 30. In other words, standardization of \( S \) leads to
\[
\frac{S - \mu_S}{\sigma_S} \approx Z
\]
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