1. Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.06 fluid ounces. What is the standard deviation of the average fill volume of 17 bags?
2. The viscosity of a fluid can be measured in an experiment by dropping a small ball into a calibrated tube containing the fluid and observing the random variableX, the time it takes for the ball to drop the measured distance. Assume that X is normally distributed with a mean of 20 seconds and a standard deviation of 28.1 second for a particular type of liquid. What is the probability that the average time of 20 experiments will be less than 15.6 seconds?
3. A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 70.2 psi and standard deviation 23.9 psi. Find the probability that a random sample of 8 fiber specimens will have sample mean tensile strength that exceeds 76.86 psi.
4. The amount of time a customer spends waiting at an airport check-in counter is a random variable with mean 8.6 minutes and standard deviation 4.9 minutes. Suppose that a random sample of 6 customers is observed. Find the probability that the average time waiting in line for these customers is between 7.2 and 8.8 minutes.
5. The photoresist thickness in semiconductor manufacturing has a mean of 11.1 micrometers and a standard deviation of 1.6 micrometer. Assume that the thickness is normally distributed and that the thickness of different wafers are independent. Determine the number of wafers that need to be measured such that the probability that the average thickness exceeds 9 micrometers is 0.049. Give your answer to two decimal places.