1. ## Standard Devitation Help

Hello again,
I have three questions here based on standard deviation that I either don't understand or am don't understanding key concepts.
The first question is a word problem:

"When reporting results to head office, Janice was told to make sure that the mean is 100 and the standard deviation is 10. When she calculated these statistical measures, she found the actual standard deviation to be 8.4 and the mean to be 106.5. Explain what Janice has to do before sending in her results to head office"
Here I just don't understand what could be done, and it makes me want to smash my head into the wall just like that guy.

"Krina works in a call center assisting home-computer users. The average length of a call in her center is 605 seconds. Her last call took only 569 seconds. her manager offers a bonus for calls that are handled efficiently and quickly. If a call is hand;ed more quickly than 95% of calls, a \$2 bonus is paid. What is the largest standard deviation for calls that would let Krina's latest call get the bonus? " I don't even know where to begin with this question.

The third and final question is:
"A biology teacher recorded the lung capacity of each 16-year-old in her school. The teacher determined that the values were normally distributed with a mean of 3500 mL and a standard deviation of 300 mL. If 23% of the 16-year-olds lung capacities were less than Samantha's, what is Samantha's lung capacity?"
I think I know how to answer it, but every time I try I end up with some absurd number.

Thanks for help with any of these in advance.

2. Originally Posted by Fishsticks
Hello again,
I have three questions here based on standard deviation that I either don't understand or am don't understanding key concepts.
The first question is a word problem:

"When reporting results to head office, Janice was told to make sure that the mean is 100 and the standard deviation is 10. When she calculated these statistical measures, she found the actual standard deviation to be 8.4 and the mean to be 106.5. Explain what Janice has to do before sending in her results to head office"
Here I just don't understand what could be done, and it makes me want to smash my head into the wall just like that guy.
You are going to modify the marks to have mean $100$ and SD $10$, this is the equvalent of marking an exam on a curve.

Let $x_i,\ i=1, 2, ..., n$ be the results, then the normalised results are:

$
y_i=100+(x_i-106.5)(10/8.4)
$

The idea is that $x_i-106.5$ has mean $0$ and SD $8.4$, so $(x_i-106.5)(10/8.4)$ has mean $0$ and SD $10$, so $y_i$ has mean $100$ and SD $10$.

RonL

3. Thank you very much for that, sir, cheers.
I am going to take another good stab at the other questions tomorrow. I'm sure I'm going to come up with a feasible solution right when I'm about to fall asleep and have to try it again.