Class Notes (1,100,000)
CA (630,000)
UTSG (50,000)
MAT (4,000)
MAT136H1 (900)
all (200)
Lecture

MAT136H1 Lecture Notes - Standard Deviation


Department
Mathematics
Course Code
MAT136H1
Professor
all

This preview shows half of the first page. to view the full 1 pages of the document.
8.5 Challenging Integral Applications
Probability Applications
Question #4 (Medium): Normal Distribution
Strategy
Normal distribution has its probability density function as  
 
, where is the mean
and the standard deviation.
Sample Question
Average amount of money spent on groceries for a single adult is shown to be $300 per month with
standard deviation of $80 according to a random city survey, and it is normally distributed.
1) What is the probability that an adult chosen at random spends over $500 per month?
2) What percentage of the city population spend less than $200 on groceries per month?
Solution
Most of survey results can be reflected unto normal distribution. Here, , and   , therefore
the pdf is
 

 

1) The probability that money spent is over $500 is:         
 
     

. This cannot be simply evaluated by taking
the integral by hand, but by either plugging into the computer calculator, or looking up normal
distribution table. Therefore,    
2) The percentage that the money spent is less than $200 is:

 
  

Therefore, the percentage of people spending less than $200 on groceries per month is .
You're Reading a Preview

Unlock to view full version