Question

Phone bills from the residents of the city have a mean of $64 and a standard deviation of $9. Random samples of 100 phone bills are drawn from this

population. Find the mean and standard error of the sampling distribution.
O mean is 6.4: standard error is 9
O mean is 64; standard error is 9
O mean is 6.4: standard error is.9
O mean is 64: standard error is.9

Answer 1

The mean of the sampling distribution is $64 and the standard error is $0.9.

Step-by-step explanation:

In this question, we are given that the phone bills from the residents of the city have a mean of $64 and a standard deviation of $9. We are also told that random samples of 100 phone bills are drawn from this population. We need to find the mean and standard error of the sampling distribution.

The mean of the sampling distribution will be the same as the mean of the population, which in this case is $64. This is because the sampling distribution represents the average of the samples, and the average of the samples should be equal to the average of the population.

The standard error of the sampling distribution can be calculated using the formula: standard error (SE) = population standard deviation / square root of sample size. In this case, the population standard deviation is $9 and the sample size is 100. So, the standard error is $9 / sqrt(100) = $9 / 10 = $0.9.

Answer 2

Mean of 64 and standard error of 0.9.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Phone bills from the residents of the city have a mean of $64 and a standard deviation of $9. Sample of 10.

By the Central Limit Theorem, the mean is 64 and the standard error is
`s = (9)/(√(100)) = (9)/(10) = 0.9`

So mean of 64 and standard error of 0.9.