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Normal Probability

Please explain solutions for #21, 22.

A final Math exam has a normal distribution with mean 73 and standard deviation 3.5.

21- If one student is randomly selected, find the probability that his score be less than 71:

A) 0.7158 B) 0.2843 C) 0.4934 D) 0.6432

22- If 25 students are randomly selected, find the probability that the mean of their scores be less than 71:

A) 0.9930 B) 0.9979 C) 0.0021 D) 0.0021

23- Why can the Central Limit be applied in question #22, if the sample size doesn't exceed 30?

A) Because the theorem is easy to apply
B) Because the population has a Normal distribution
C) Because this theorem is very important in inferential statistics.
D) Because this theorem apply only in scores distributions.

Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.