Pregunta
The proportion of homes in Florida owned by investors rather than homeowners is
. Consider a sampling distribution where
.
Can a normal distribution approximation be used for the sampling distribution of sample proportions?
No, a normal distribution approximation can’t be used .
Can a normal distribution approximation be used for the sampling distribution of sample proportions?
No, a normal distribution approximation can’t be used .
Ask by Horton Frazier. in the United States
Mar 15,2025
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Solución
-
Given that the proportion is
and the sample size is , calculate -
-
Check the conditions for using the normal approximation for a binomial distribution, which require both:
-
-
Since
and are both greater than 10, the normal approximation is valid. -
Therefore, a normal distribution approximation can be used for the sampling distribution of the sample proportion.
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Extra Insights
In this scenario, we can calculate
and
to determine the sampling distribution’s viability. Here,
and
. Thus,
. Similarly,
.
Both
and
need to be at least 10 for the normal approximation to be applicable. Since both values exceed 10, a normal distribution approximation can be used for the sampling distribution of sample proportions after all!

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