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?

Question

Mathematics

Alfred Bird

28 August, 18:36

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?

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Amani Villanueva · 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