What theorem will let us treat T and M as approximately normal random variables? Central Limit Theorem301 Theorem Chebychev's TheoremLaw of Large NumbersMonte Carlo TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T
The mean weight of a single newborn baby at City Central Hospital is 111.2 ounces with a standard deviation of 16.05 ounces. Let us assume that the weight, X, of any baby born at City Central is independent of the weight of any other baby born at City Central. We will not consider multiple births. City General expects 1111 babies to be born in 2022. Suppose we look at the weight of each newborn baby at City General in 2022. Let M be the random variable representing the mean weight of all the 1111 newborn babies expected. Let T = the random variable representing the total weight of all the 1111 newborn babies expected.
a) What theorem will let us treat T and M as approximately normal random variables?
b) What is the
c) What is the standard deviation of T?
d) If TK is the total weight of the 1111 babies measured in pounds, then what is the standard deviation of TK?
e) What is the approximate probability that T is greater than 125000 ounces?
f) What is the standard deviation of M?
g) What is the approximate probability M is between 110 and 112 ounces?
h) City General has a baby elevator that moves babies between floors. The elevator will need major repairs if (and only if) the total weight (TW) of the 1111 babies is too large. Their insurance company charges them based on the probability that the baby elevator needs major repairs. For low rates, the probability of a major repair being needed must be less and or equal to 12%. What total weight TW will be the greatest weight for which the hospital gets low rates?
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