# 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 This solution is **FREE** courtesy of BrainMass!

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.

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