Comme un jeu

Lower Limit: Upper Limit: Mean (μ): Standard Deviation (σ):

A coffee machine is supposed to dispense 200 ml of coffee per cup. However, the amount varies slightly from cup to cup.
Let \(X_i\) be the volume of a single cup. Based on quality control, the volume has a mean \(\mu = 200\) ml and a standard deviation \(\sigma = 15\) ml.
A health inspector takes a random sample of 50 cups. Let \(\overline{X}_{50}\) be the average volume of these 50 cups.

Find the expected value of the sample mean, \(E(\overline{X}_{50})\).
Calculate the standard deviation for a single cup (\(\sigma\)), and then find the standard deviation of the sample mean, \(\sigma(\overline{X}_{50})\).
The distribution of a single cup is not necessarily normal. Can we assume the sample mean \(\overline{X}_{50}\) is normally distributed? Explain.
Find the probability that the average volume of the sample is less than 195 ml.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.