Question

A machine used to fill​ gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents. The sample mean of the cans is ounces. Does the machine need to be​ reset? Explain your reasoning.

Answer 1

Answer:

No, It is not necessary that the machine has to be reset

Step-by-step explanation:

The full question is "A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 126 ounces and a standard deviation of 0.40 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 125.9 ounces. Does the machine need to be reset?"

The amount of paint that has dispensed has a mean of 126 ounces and a standard deviation of 0.40 ounce.

A sample of 40 cans is taken and this has a sample mean of 125.9 ounces

The z score is:

Z  = Х  - ц / (б/$\sqrt{n}$)

Z = 125.9 - 126  / 0.4 /$\sqrt{40}$

Z = -0.1  / 0.0632

Z = -1.58

The value of z-score is –1.58. It is not necessary that the machine has to be reset as, the z score value of randomly sampled 40 cans with a mean equal to 125.9 ounces is likely and lies within 2 standard deviations of the mean.