According to a study conducted in one city, 25% of adults in the city have credit card debts of more than $2000. A simple random sample of n equals 150 adults is obtained from the city. Describe the sampling distribution of ModifyingAbove p with caret, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary.

Following are the calculation to the given value:

Given:

Based on one town's study, the population percentage of adults in the city had credit card bills totaling and over

A city-wide sample of adults was recruited  

Solution:

For step 1:

To get the sampling distribution of probability value , we should first determine whether the sample is sufficient using the following two conditions:

The two conditions are fulfilled. We understand from the "Central limit theorem" that the as being is roughly normally distributed with the mean   and the standard deviation along with

 Therefore the 2 conditions which satisfy the proportion of sample that were normally distributed by the mean and the standard deviation

 For step 2:

Sample proportion mean

 For step 3:  

The sample proportion  of the standard deviation:    

Since the distribution of the sample proportion that is is adults which has to credit card debts of more than is approximately normal; .

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The sampling distribution of 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:

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

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:

The standard deviation is:

Thus, the sampling distribution of is N (0.25, 0.0354²).

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step-by-step explanation: