Question: Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations, That is, unusual values are either less than \(\mu -2\sigma \) or greater than \(\mu +2\sigma \)

A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual get 539 consumers who recognize the Dull Computer Company name?

Solution: The mean is computed as:

Now, the variance is computed as:

Finally, the standard deviation is computed as:

The usual is therefore: (544-2*13.1939, 544+2*13.1939 = (517.6122, 570.3878), which means that 539 is not unusual because it is contained by the usual range.

Use the Poisson Distribution to find the indicated probability.

25) The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.1. Find the probability that in a randomly selected year, the number of lightning strikes is 0.