A dispensing machine at a ketchup factory has been set to fill ketchup bottles according to a normal distribution with a process mean of 40 ounces and process standard deviation of 0.18 ounces. Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
a. The quality department has a requirement that individual bottles of ketchup should contain between 39.65 ounces and 40.35 ounces. What is the probability that a randomly selected bottle will violate this requirement? Probability =
b. Between how many ounces of ketchup would you expect 95% of the individual bottles to contain? Lower value = ounces. Upper value = ounces.
c. The quality department also selects a random sample of four bottles every hour and weighs the ketchup content. The requirement is that the sample mean content of these four bottles must be between 39.85 ounces and 40.15 ounces. What is the probability that a random sample of four bottles will violate this requirement? Probability =
d. Between how many ounces of ketchup would you expect 95% of the sample means for the n = 4 bottles to contain? Lower value = ounces. Upper value = ounces.
e. Suppose the dispensing machine is experiencing a problem. The process mean has drifted down to 39.94 ounces and the process standard deviation has increased to 0.20 ounces. Using these revised mean and standard deviation values, what is the probability that a sample mean for a random sample of four bottles will violate the 39.85 ounce to 40.15 ounce requirement? Probability =