Page 151 - Probability Demystified

140 CHAPTER 8 Other Probability Distributions

Note: The computations require a scientific calculator. Also, tables for
values used in the Poisson distribution are available in some statistics
textbooks.

EXAMPLE: If there are 150 typographical errors randomly distributed in a
600-page manuscript, find the probability that any given page has exactly two
errors.

SOLUTION:
1
Find the mean numbers of errors: ¼ 150 ¼ or 0.25. In other words, there is
600 4
an average of 0.25 errors per page. In this case, x ¼ 2, so the probability of
selecting a page with exactly two errors is

x 0:25 2
e ð2:7183Þ ð0:25Þ
¼ ¼ 0:024
x! 2!
Hence the probability of two errors is about 2.4%.

EXAMPLE: A hotline with a toll-free number receives an average of 4 calls
per hour. For any given hour, find the probability that it will receive exactly
6 calls.

SOLUTION:

The mean ¼ 4 and x ¼ 6. The probability is
x
e ð2:7183Þ 4 ð4Þ 6
¼ ¼ 0:104
x! 6!
Hence there is about a 10.4% chance that the hotline will receive 6 calls.

EXAMPLE: A videotape has an average of two defects for every 1000 feet.
Find the probability that in a length of 2000 feet, there are 5 defects.

SOLUTION:
If there are 2 defects per 1000 feet, then the mean number of defects for 2000
feet would be 2 2 ¼ 4. In this case, x ¼ 5. The probability then is
x
e ð2:7183Þ 4 4 5
¼ ¼ 0:156
x! 5!