A normal distribution has a mean of mu 80 and a standard de

A normal distribution has a mean of mu = 80 and a standard deviation of sigma = 15. For each of the following samples, compute the z-score for the sample mean, and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size. M = 84 for n = 9 scores: z = , which is _______________ value for a sample of this size. M = 84 for n = 100 scores: z = ,which is _______________ value for a sample of this size.

Solution

Answer:

(a)

Here, mean = 80, sd = 15
So, z-score = ((X-mu)/sd) = ((84-80)/15) = 4/15 = 0.266667
P (z<0.267) = 0.605265419

(b)

Here, mean = 80, sd = 15 and n = 100
So, z-score = ((X-mu)/sd) = ((84-80)/(15/sqrt(100)) = 40/15 = 2.66667
P (z<2.67) = 0.996207438

So for both cases sample mean is a typical