Question

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. the reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. suppose the reported values are the true mean and standard deviation for the population of subjects in the study. if a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

Answer 1

It can be considered that the distribution of the sample is normal, based on the central limit theorem, where the sigma of the sample is:σ / root (n).
 The mean of the sample is:
 μm = μ
 So:
 P (X> 11) = P (Z> Zo).
 Where Z follows a standard normal distribution and
 Zo = (μm-μ) / (σ / root (n))
 Zo = (11-10.2) / (16 / root (144)).
 Zo = 0.6
 From the table for the standard normal distribution we have to:
 P (Z> 0.6) = 0.2743