Question

21 A e À AS A A.D.A. AaBbcDX AalbCD AaBbc AaBbce KAU AIBOL 1 Normal T No Spac. Heading 1 Heading 2 Title Subtit Styles Paragraph 2. A random sample is obtained from a normal population with a mean of ji = 90 and standard deviation o = 40. The sample mean M = 85. a. Is this a representative sample mean or an extreme value for a sample of n = 16? How do you know?

Answer 1

Using the Central limit theorem, the distribution of sample means of sample size n = 16 is obtained here as:

$\bar X \sim N(\mu = 90, \sigma = \frac{40}{\sqrt{16}})$

$\bar X \sim N(\mu = 90, \sigma = 10)$

The Z score for the given sample mean value of 85 here is computed as:

$z = \frac{M -\mu}{\sigma} = \frac{85 - 90}{10} = -0.5$

As the given value is within 0.5 standard deviations from the mean, therefore the given value is representative sample mean and not an extreme value.