MAT136H1 Lecture Notes - Standard Deviation
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8.5 Challenging Integral Applications
Question #4 (Medium): Normal Distribution
Normal distribution has its probability density function as
, where is the mean
and the standard deviation.
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?
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 .
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