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Answer:
The sampling distribution of is <em>N</em> (0.25, 0.0354²).
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
Let <em>p</em> = proportion of adults in the city having credit card debts of more than $2000.
It is provided that the proportion of adults in the city having credit card debts of more than $2000 is, <em>p</em> = 0.25.
A random sample of size <em>n</em> = 150 is selected from the city.
Since <em>n</em> = 150 > 30 the Central limit theorem can be used to approximate the distribution of <em>p</em> by the Normal distribution.
The mean is:
The standard deviation is:
Thus, the sampling distribution of is <em>N</em> (0.25, 0.0354²).