Sulfur compounds such as dimethyl sulfide (DMS) are sometimes present in wine. DMS causes "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of DMS that the human nose can detect. Different people have different thresholds, so we start by asking about the DMS threshold in the population of all adults. Extensive studies have found that the DMS odor threshold of adults follows roughly a normal distribution with mean μ = 23.8 micrograms per liter and standard deviation σ = 7.4 micrograms per liter.
In an experiment, we present tasters with both natural wine and the same wine spiked with DMS at different concentrations to find the lowest concentration at which they identify the spiked wine. Here are the odor thresholds (measured in micrograms of DMS per liter of wine) for 10 randomly chosen subjects.
25 30 25 28 30 34 36 34 36 35
The mean threshold for these subject is x = 31.3. Find the probability of getting a sample mean even farther away from μ than x = 31.3.