Assume that the fill, X, of a water filling machine is 12.2 with a standard deviation of 0.1 with the measurements being in liquid ounces. Assume X is a normal random variable. Suppose we independently take 50 such measurements, say X1, X2, .., X50. Let M be the sample mean of the 50 measurements. Let S be the sum of the 50 measurements. a) What is the probability that X < 12? b) What is the probability that at least one of the 50 measurements is less than 12? c) What is the expected value of S-(50 * 12.2) ? d) What is the standard deviation of S- (50 * 12.2) ? e) What is the probability that S- (50 * 12.2) >1? f) What is the probability that S- (50 × 12.2) < -0.5? g) What is the expected value of M? h) What is the standard deviation of M-12.2? i) What is the probability that M-12.2>.01? j) What is the standard deviation of 50*(M-12.2)? k) What is the variance of 50*(M-12.2)? l) If the probability of X > k is equal to .05 then what is k.?
Assume that the fill, X, of a water filling machine is 12.2 with a standard deviation of 0.1 with the measurements being in liquid ounces. Assume X is a normal random variable. Suppose we independently take 50 such measurements, say X1, X2,
.., X50. Let M be the sample mean of the 50 measurements. Let S be the sum of the 50 measurements.
a) What is the probability that X < 12?
b) What is the probability that at least one of the 50 measurements is less than 12?
c) What is the
d) What is the standard deviation of S- (50 * 12.2) ?
e) What is the probability that S- (50 * 12.2) >1?
f) What is the probability that S- (50 × 12.2) < -0.5?
g) What is the expected value of M?
h) What is the standard deviation of M-12.2?
i) What is the probability that M-12.2>.01?
j) What is the standard deviation of 50*(M-12.2)?
k) What is the variance of 50*(M-12.2)?
l) If the probability of X > k is equal to .05 then what is k.?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
