What theorem will let us treat T and M as approximately normal random variables? Monte Carlo TheoremLaw of Large Numbers 301 TheoremCentral Limit TheoremChebychev's TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 1400?
The fracture strength of bi-tempered glass averages 14.03 (measured in thousands of pounds per square inch) and has standard deviation 2. Suppose we randomly select 100 pieces of bi-tempered glass. Let M be the random variable representing the mean fracture strength of the 100 selected pieces. Let T be the random variable representing the sum of the fracture strengths of the 100 selected pieces. Using R and write the code out
a) What theorem will let us treat T and M as approximately normal random variables?
b) What is the expected value of T?
c) What is the standard deviation of T?
d) What is the approximate probability that T is greater than 1400?
e) What is the 98th percentile of the approximate distribution of T?
f) What is the standard deviation of M?
g) What is the approximate probability M is greater than 13.99?
h) What is the variance of 93M?
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