# 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.

https://brainmass.com/statistics/probability/probability-distributions-math-exam-scores-414559

#### Solution Preview

Please see the attachment.

Probability Math Exam

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) ...

#### 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.