# Statistics and integration problem

1. Aug 4, 2011

### Boogieface

Statistics and integration problem (urgent)

can anyone help me with (6)?

#### Attached Files:

File size:
30.4 KB
Views:
97
File size:
40.6 KB
Views:
84
• ###### 04082011530.jpg
File size:
35.1 KB
Views:
87
Last edited: Aug 4, 2011
2. Aug 4, 2011

### lanedance

what is the cumulative probability of a profit < 0?

3. Aug 4, 2011

### Boogieface

sorry, what does cumulative probability mean?
In (3), I assumed the region is when the x axis is negative which is 0.025 probabiltiy.
In (4), I used (3) as the same answer.
In (5), I used the calculator to work out putting integral with -10 lower bound and 0 upper bound. I got 0.028
but it doesn't make much sense at all...

4. Aug 4, 2011

### lanedance

so you want to find P(X<=0) where X is the profit

Knowing it is a normal distribution with mean 2 and SD 1, this is the probability of being 2 D's from the mean

this means it should be a about 2.2-2.3% probability, though you should be able to look it up in a table no worries to get an exact number - also see below
http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

as mentioned for a 4% probability we intepret t his as a (1 in 1/0.04=25year ) event

what does this translate into for a 2.3% event (or whatever number you come up with?)

5. Aug 4, 2011

### Boogieface

sorry, I still don't get the idea how to change it into years that the bank would make a loss.

6. Aug 4, 2011

### lanedance

For the 4% case
1/25 = 0.04 = 4%
work backwards from that

The idea is that in 1 year in 25 is 4% of that time period. If the probability of an event is 4%, we would expect it to occurs 1 year in every 25 on average

7. Aug 4, 2011

### Boogieface

what i have done is, use 1 divided by the answer of (5) P = 0.0228

8. Aug 4, 2011

### lanedance

sounds like a good idea - do you get a reasonable answer?