Question

The amount people who pay for electric service varies quite a bit, but the mean monthly fee is $168 and the standard deviation is $34. The distribution is not Normal. Many people pay about $90 in rural areas of the country and about $150 in urban areas of the country, but some pay much more. A sample survey is designed to ask a simple random sample of 1,200 people how much they pay for electric services.

I need the mean and standard deviation of the sample distribution and i need to know the shape of the sampling distribution

Answer 1

The mean of the sample distribution is $168, and standard deviation of the sample distribution is 0.98.

The shape of the sampling distribution of sample mean is aproximately normally distributed due to sample size is larger than 30 which is 1,200

Explanation:

According to the given data the mean monthly fee is $168, therefore, the mean of the sampling distribution of sample mean is:

μx=μ

=$168

The mean of the sampling distribution of sample means is $168

The standard deviation of the sampling distribution of sample mean is:

σx=σ/√n

σx=$34/√1,200

σx=0.98

The standard deviation of the sampling distribution of sample mean is 0.98

The shape of the sampling distribution of sample mean is aproximately normally distributed due to sample size is larger than 30 which is 1,200