The grades on the last history exam had a mean of 75%. Assume the population of grades on history exams is known to be normally distributed with a standard deviation of 7. What percent of students earn a score between 70% and 82%?

Question

kirbykirby · Answer

Let $X$ be the grades of the history exam. Then, you are asked to find $P(70 < X < 82)$. WHat you can do is standardize X to get:
$$X=\frac{X-\mu}{\sigma} $$ and obtain:
$$ P(70 < X < 82) = P\left( \frac{70-75}{7}<\frac{X-75}{7}<\frac{82-75}{7}\right)\
=P(-0.71<Z<1)$$ and then use a standard normal table to find the probability

anonymous · Answer

0.6285

 0.6101

 0.6024

 0.5892

anonymous · Answer

So we don't know what x is?

anonymous · Answer

@kirbykirby

kirbykirby · Answer

Well X is a random variable. You standardize it as above to find a z-score. Then you find the probability using standard normal tables.

anonymous · Answer

I'm absolutely awful at this. Can you help me go through it step by step. I'm having a very hard time grasping the concept.

anonymous · Answer

@kirbykirby

kirbykirby · Answer

So you have X being certain values for the history grades. It has a mean of 75, and standard deviation 7. So, the normal curve will look smtg like this: |dw:1403542425591:dw|