The percentage of Americans that have blue eyes is approximately 17%, so the probability that a randomly chosen American has blue eyes is 0.17. Let the random variable B = the number of blue eyed people in a SRS of 200 Americans.

1. The value 33 is near the mean, but its probability isn't too big. Why?

2. Is the probability of the event "the sample contains 50 or fewer blue eyed people" likely or unlikely to occur. Explain with calculations and without in sentences.

3. Calculate the probability of the event "the sample contains 50 or fewer blue eyed people".

4. Calculate the interval [ , + ]. Round off the values to the nearest integer, and calculate the probability that the number of blue eyed people in the sample is in this interval.

5. Calculate the interval [ 2, + 2] Round off the values to the nearest integer, and calculate the probability that the number of blue eyed people in the sample is in this interval.

-Based on the answers to 4 and 5, does the distribution of B follow the Empirical Rule?

6. Write the event "the sample contains exactly 33 blue eyed people" using symbols, including the random variable B.