MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:Suppose \( X \) is a normal random variable with an expected value of 21.21 and a standard deviation of 3.33. We take a random sample of size \( n \) from the distribution of \( X \). Let \( \overline{X} \) be the sample mean. Use R to determine the following:
a) Find the probability \( P(X < 23.1) \)
- Result: 0.7148357
b) Find the probability \( P(\overline{X} < 23.1) \) when \( n = 4 \)
- Result: 0.8718406
c) Find the probability \( P(\overline{X} < 23.1) \) when \( n = 25 \)
- Result: 0.997729
d) What is the probability \( P(22 < \overline{X} < 23.5) \) when \( n = 25 \)
- Result: 0.1174819
e) What is the standard deviation of \( \overline{X} \) when \( n = 39 \)
- (Calculate here)
f) What is the probability that \( X_1 + X_2 + \ldots + X_{17} > 361.57 \)?
- (Calculate here)
g) Copy your R script for the above into the text box here.
- (Provide script here)
This task involves calculating probabilities and the standard deviation of the sample mean using the normal distribution and a statistical programming language, R.
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