Question

Triola Chapter6 Normal Distribution: Problem (1 point) Suppose a random variable x is normally distributed with μ=24.5 and σ=5.6. According to the Central Limit Theorem, for samples of size 7: (a) The mean of the sampling distribution for xˉ is: (b) The standard deviation of the sampling distribution for xˉ is:

Answer 1

The mean of the sampling distribution for x-bar is 24.5. The standard deviation of the sampling distribution for x-bar is 5.6 divided by the square root of 7.

Step-by-step explanation:

The Central Limit Theorem states that for samples of sufficient size, the distribution of sample means will be normal, even if the population distribution is not normal.

In this problem, the sample size is 7.

According to the Central Limit Theorem, the mean of the sampling distribution for x-bar (sample mean) is equal to the population mean.

Therefore, the mean of the sampling distribution for x-bar is 24.5.

The standard deviation of the sampling distribution for x-bar is equal to the population standard deviation divided by the square root of the sample size.

So, the standard deviation of the sampling distribution for x-bar is 5.6 divided by the square root of 7.