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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.

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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) 0.6432
Hint:
Let X be the score obtained in the final Math exam. Given that X is normal with mean µ = 73 and standard deviation  = 3.5.
We need P (X < 71). Standardizing the variable X using and from standard normal tables, we have
P (X < 71) = = P (Z < -0.57) = 0.2843

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
Hint:
Since X ~ N (µ, σ), . That is, or ~ N (73, 0.7). Standardizing using and from standard normal tables, we have,
P ( < 71) = = P (Z < -2.86) = 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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 4, 2022, 3:27 pm ad1c9bdddf>
https://brainmass.com/statistics/probability/probability-distributions-math-exam-scores-414559