EXAMPLE 44The normal approximation to the binomial distribution

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The Centers for Disease Control and Prevention reported that 20% of preschool chil dren lack required immunizations, thereby putting themselves and their classmates at risk. For a group of children with , the binomial probability distribution is shown in Figure 72.

  1. Verify that this distribution can be approximated by a normal distribution.
  2. Find the mean and standard deviation of this normal distribution.

Solution

  1. The normal approximation is valid if and . Substituting and , we get

    Thus, the normal approximation is valid.

  2. The mean and standard deviation of the normal distribution are

NOW YOU CAN DO

Exercises 3–8.