Asked by Mariya&Eliza George on May 29, 2024

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As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

A) the sample size n is greater than 30
B) the sample size n is greater than 100
C) the population proportion p is close to 0.50
D) the underlying population is normal
E) np and n(1 - p) are both greater than or equal to 5

Sampling Distribution

The probability distribution of a given statistic based on a large number of samples drawn from a specific population, used to estimate population parameters.

Sample Proportion

The sample proportion is a statistic that estimates the proportion of elements in a population that have a certain characteristic, based on a sample from that population.

Population Proportion

A measure that represents the fraction of members in a population that have a particular property or attribute.

  • Recognize the conditions under which the normal approximation to the binomial distribution is appropriate.
  • Understand the importance of sample size in approximating binomial distributions with normal distributions.
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KM
Karla Muñoz DueñasMay 31, 2024
Final Answer :
E
Explanation :
The best choice is E because it is the correct condition for using the normal distribution to approximate the sampling distribution of the sample proportion. If np and n(1-p) are both greater than or equal to 5, then the sample size is large enough to assume that the sampling distribution is approximately normal regardless of the underlying population distribution. This condition ensures that there are enough successes and failures in the sample to justify the normal approximation.