Why is it important to use the correction for continuity when ...

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Why is it important to use the correction for continuity when approximating binomial probabilities with the normal distribution?

Question 2

The national sales manager of Fast Grow Corp is working on next year's budget projections. He knows that the population standard deviation is 17.66 . To estimate the daily per diem cost for outside sales people, he has taken a random sample of 36 individual expense accounts and found a mean of 90.29 . The 91.08 percent confidence interval for the per diem expense is:
 a. 86.45 to 94.13.
  b. 60.27 to 120.37.
  c. 85.29 to 95.29.
  d. 74.43 to 107.9.
  e. 84.32 to 96.26.

[brittanywood]

Answer to Question 1

Because the binomial distribution has gaps between possible values of x (since it is discrete), while the normal distribution is continuous, the normal approximation to the binomial involves a correction for continuity. The correction consists of expanding each possible value of the discrete random variable x by 0.5 in each direction.

Answer to Question 2

C

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Gracias!

[FergA]

TYSM