Question

A machine is set to fill milk containers with a mean of 63 ounces and a standard deviation of 0.11 ounce. A random sample of 40 containers has a mean of 63.05 ounces. The machine needs to be reset when the mean of a random sample is unusual. Does the machine need to be reset? Explain. because the z-score within the range of a usual event, namely within of the mean of the sample means. (Round to two decimal places as needed.)

Answer 1

The machine does not need to be reset because the sample mean is not unusual.

Step-by-step explanation:

To determine if the machine needs to be reset, we need to calculate the z-score of the sample mean and compare it to the range of usual events.

The z-score can be calculated using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

• x is the sample mean (63.05)
• μ is the population mean (63)
• σ is the population standard deviation (0.11)
• n is the sample size (40)

Plugging in the values, we get:

z = (63.05 - 63) / (0.11 / sqrt(40)) ≈ 0.1642

The z-score of 0.1642 falls within the range of a usual event, meaning that the sample mean is not unusual. Therefore, the machine does not need to be reset.