Hello,

I have a few questions that I'm wondering if I could get any help on:

1) A student recieved a standardized Z-score on a test that was -0.57. What does this score tell about how this student scored in relation to the rest of the class?

When I looked up -.57 on the Z-score table it gives me .28, or I'm assuming, 28%. So does this mean that she did better than 28% of her class, or worse than 28% of her class?

Mr F says: Better. Draw the curve and see where she is.
2) A large college class has 900 students, broken down into section meetings with 30 students each. On the final exam, scores followed a normal distribution with an average of 63 and a standard deviation of 20.

a) if you randomly select one of these students, what is the probability that the selected student scored between 56 and 70 on the exam?

would the answer be 27%?

Mr F says: Yes.
b)if we consider a section of 30 students as a random sample from this population, will the probability that the average for the section is between 56 and 70 be higher or lower or the same as what you calculated in the previous question?

On this part, it would be the same right? Since it doesnt say anything about certain sections, I would assume the average and standard deviation apply the same way.

Mr F says: The sample average $\displaystyle {\color{red}\bar{X}}$ follows a normal distribution with mean 63 and standard deviation $\displaystyle {\color{red}\frac{20}{\sqrt{30}}}$. Calculate $\displaystyle {\color{red} \Pr(56 < \bar{X} < 70 )}$.
3)Find the mean of a normally distributed random variable with a standard deviation of 8 if 95.99% of all the values are less than 17.

I would appreciate any help I can get, I'm feeling lost on some of this