Solution to Problem 3

For each of the following probability statements involving the binomial distribution and variable r number of successes, write down the corresponding probability statement that uses the normal distribution variable X.  Make sure you use the continuity correction.
  1.  P(r < 18)

    Since r  <  18 and r  <  17 are the same for this binomial variable, the continuity correction gives P(x < 17.5).


  2.  P(r > 59)

    Since r  >  59 and r  >  60 are the same for this binomial variable, the continuity correction gives P(x > 59.5).


  3.  P(r < 22)

    Since r  <  22 and r  <  23 are the same for this binomial variable, the continuity correction gives P(x < 22.5).


  4.  P(r > 37)

    Since r  >  37 and r  >  36 are the same for this binomial variable, the continuity correction gives P(x > 36.5).


  5. P(11 < r < 19)

    Since 11  >  r and 10  >  r are the same and r  <  19 and r  <  20 are the same for this binomial variable, the continuity correction gives P(10.5 < x < 19.5).

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