Question

a sample random sample of 150 adults is obtained and each persons red blood cell count (in cells per microliter) is measured. the sample mean is 4.63. the population standard deviation for red blood cell counts is 0.54. which of the following is true regarding the distribution of sample means?
choose the correct answer below.
o a. the distribution of the population data is not given. therefore, the shape of the distribution of sample means cannot be known for sure.
o b. even though the distribution of the population data is not given, the distribution of sample means will be approximately normal because the sample size is large enough according to the central limit theorem.
o c. the distribution of sample means will not be normal since the sample size is too large.
o d. the distribution of the population data is not given. therefore, the distribution of sample means will not be normal.

Explanation:

The Central Limit Theorem (CLT) states that if we have a sample of size \(n\) from any population (regardless of the population's distribution), when \(n\) is large (usually \(n\geq 30\)), the sampling distribution of the sample mean \(\bar{X}\) is approximately normal. Here, the sample size \(n = 150\geq30\).

Answer:

B. Even though the distribution of the population data is not given, the distribution of sample means will be approximately normal because the sample size is large enough according to the Central Limit Theorem.