Question

The weight specification for packets of noodles is 100± 5 grams. Inspection has revealed that 95% of the packets are within the specifications. However, the process is not centered at 100 grams. The packet-filling process is in a state of statistical control and the packet weights are normally distributed with a standard deviation of 1.2 grams.

Find the value for process mean so that only one packet in 10,000 falls below the lower specification.

Answer 1

To find the mean value for the packet-filling process so that only one packet in 10,000 falls below the lower specification, calculate the z-score corresponding to a probability of 0.0001. The mean weight is approximately 95.5452 grams.

Step-by-step explanation:

To find the mean value for the packet-filling process so that only one packet in 10,000 falls below the lower specification, we need to calculate the z-score corresponding to a probability of 0.0001. The z-score represents how many standard deviations a value is from the mean, and we can use a standard normal distribution table or a calculator to find this value.

Using the standard normal distribution table, we find that the z-score for a probability of 0.0001 is approximately -3.719. We can then use this z-score to find the corresponding packet weight using the formula:

X = μ + (z * σ)

Where X is the weight, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values given in the question (standard deviation of 1.2 grams and a probability of 0.0001), we can calculate the mean weight:

X = 100 + (-3.719 * 1.2) = 95.5452 grams