The length, X, of a lionfish is a normally distributed random variable with a mean of 13.5 inches and a standard deviation of 2.4 inches. Suppose that we measure the lengths of 150 randomly chosen lionfish. Let M be the sample mean of the 150-length measurements. Let S be the sum of the 150 length measurements. a) What is the probability that X < 9.3? b) What is the probability that X > 9.3? c) What is the probability that all of the 150 measurements are greater than 9.3? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-150*13.5 >10? g) What is the standard deviation of S-150*13.5 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >13.6? k) What is the standard deviation of 30*M? l) If the probability of X > k is equal to .8, then what is k?
The length, X, of a lionfish is a
a) What is the
b) What is the probability that X > 9.3?
c) What is the probability that all of the 150 measurements are greater than 9.3?
d) What is the
e) What is the standard deviation of S?
f) What is the probability that S-150*13.5 >10?
g) What is the standard deviation of S-150*13.5
h) What is the expected value of M?
i) What is the standard deviation of M?
j) What is the probability that M >13.6?
k) What is the standard deviation of 30*M?
l) If the probability of X > k is equal to .8, then what is k?
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