Focus groups of 12 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group)

Focus groups of 12 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 9.5, and the standard deviation is 0.69. Would it be unusual to randomly select 12 people and find that fewer than 6 recognize the Yummy brand name? 

I think I will just talk about Alan's answer a little.

Mean=9.5

one standard deviation either side of the mean is    

Standard deviation is 0.69

$$\\9.5-0.69\;\;to\;\;9.5+0.69\\
8.81\;\;to\;\;10.19\qquad\\\$$

So approx 67% of the time there will be between 8.8 and 10.2 people who recognise the brand name.

etc

99.7% of the time the number will be between -3 and +3 standard deviation from the mean

100-99.7=0.3 and  a half of 0.3=0.15

Now 3 standard deviation below  the mean is  9.5-3*0.69 = 7.43

there is less than 0.15% chance that the number of people who recognise the product will  be less than 7.43.

So the liklihood that only 6 or less recognise the product is tiny.  It would be extremely unlikely.

Find out how many standard deviations 6 is from 9.5 and look up the probability, or, better in this case, just look at a graph of the probability density function like below (assuming the distribution is normal).

If you look at the graph, does it seem likely that fewer than 6 people would have heard of Yummy?  Strictly, the graph shouldn't go above 12, so using a normal distribution is an approximation.