# According to a study conducted in one city, 25% of adults in the city have credit card debts of

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## Answers

The sampling distribution of [tex]\hat p[/tex] is N (0.25, 0.0354²).

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 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:

[tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

Let p = 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, p = 0.25.

A random sample of size n = 150 is selected from the city.

Since n = 150 > 30 the Central limit theorem can be used to approximate the distribution of p by the Normal distribution.

The mean is:

[tex]\mu_{\hat p}=p=0.25[/tex]

The standard deviation is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.25(1-0.25)}{150}}=0.0354[/tex]

Thus, the sampling distribution of [tex]\hat p[/tex] is N (0.25, 0.0354²).

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answer is 33

step-by-step explanation: