Question

Please help i will literally give you everything I have i am inept The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85. Which of the following is true about the sampling distributions of the sample mean for the two sample sizes? A.) Both distributions are approximately normal with mean 65 and standard deviation 3.5. B.) Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85. C.) Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85. D.) Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5. E.) Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

Answer 1

Answer: the correct answer is E.) Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

Explanation:

For a normal distribution, the mean of the sampling distribution of the sample means will be equal to the population mean. In this case, the population mean is 65 inches.

However, the standard deviation of the sampling distribution of the sample means depends on the sample size. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

For the sample size of 5, the standard deviation of the sampling distribution will be (3.5 / √5) inches.

For the sample size of 85, the standard deviation of the sampling distribution will be (3.5 / √85) inches.

Based on this information, we can determine the correct option from the given choices.

Looking at the options:

A.) Both distributions are approximately normal with mean 65 and standard deviation 3.5.

This is incorrect because the standard deviation of the sampling distribution depends on the sample size.

B.) Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

This is incorrect because the standard deviation of the sampling distribution depends on the sample size.

C.) Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

This is incorrect. The standard deviation of the sampling distribution is inversely proportional to the square root of the sample size. Therefore, the standard deviation for size 5 will be smaller than that for size 85.

D.) Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.

This is incorrect because the distribution for size 5 will also be approximately normal.

E.) Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

This is the correct option. The distribution for size 85 will be approximately normal, while the distribution for size 5 will also be approximately normal but with a smaller standard deviation.