EXAMPLE 13 Minimum sample size for approximate normality

According to George Washington University, 4.3% of all vehicles on the road are large trucks. Let represent the population proportion.

  1. Find the minimum size of the samples that produces a sampling distribution of that is approximately normal.
  2. Describe the sampling distribution of if we use this minimum sample size.

Solution

  1. Using Fact 7, the minimum sample size required is the larger of either

    Here,

    419

    The larger of and is . However, it is unclear what “0.3” of a vehicle means. So we round up to the next integer: . Therefore, the minimum sample size required to produce a sampling distribution of that is approximately normal is vehicles. We confirm that this satisfies our conditions:

  2. We have and

    Because the conditions are met, the Central Limit Theorem for Proportions applies. The sampling distribution of is approximately normal .

NOW YOU CAN DO

Exercises 19–24