Question

An automated machine serves hot chocolate cups. The nominal volume of each hot chocolate cup is 300ml, with a standard deviation of 19.14 ml. A technician samples 19 cups and finds a sample mean volume of 318.34ml. What is the corresponding z-score for the difference between sample mean volume and nominal volume, rounded to 2 decimal places?

Answer 1

The corresponding z-score for the difference between the sample mean volume and nominal volume is 0.96, rounded to 2 decimal places.

Step-by-step explanation:

The z-score measures the number of standard deviations a data point is from the mean. In this case, we want to find the corresponding z-score for the difference between the sample mean volume (318.34ml) and the nominal volume (300ml).

To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the sample mean, μ is the nominal volume mean, and σ is the standard deviation. Plugging in the values, we get:

z = (318.34 - 300) / 19.14 = 0.96

Therefore, the corresponding z-score for the difference between the sample mean volume and the nominal volume is 0.96, rounded to 2 decimal places.