Mean and standard deviation of binomial distribution

Lessons

• Introduction
  $P(x)={_n}C_x \;P^x(1-p)^{n-x}$
  
  

  $n$: number of trials
  

  $x$: number of success in n trials
  

  $p$: probability of success in each trial
  

  $P(x)$: probability of getting $x$ successes (out of $n$ trials)
  
  $\cdot$ binomialpdf $(n,p,x)$
  
  $\cdot$ $\mu=np$
  
  $\cdot$ $\sigma^2=np(1-p)$
  
  $\cdot$ $\sigma= \sqrt{np(1-p)}$
  
  Range Rule of Thumb (Usual VS. Unusual):
  $\cdot$ maximum usual value $= \mu+2\sigma$
  $\cdot$ minimum usual value $= \mu-2\sigma$
  

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• 1.
  Finding the Mean and Standard Deviation
  If you roll a fair die 12 times,
  
  a)

  How many times do you expect to roll a 6?
  
  
  b)

  What is the standard deviation of rolling a 6?
  
  

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• 2.
  Dealing with a Non-Integer Mean
  How many times would you expect to roll a 6, if you rolled the die 10 times?

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• 3.
  Interpreting Mean and Standard Deviation of Binomial
  10% of accidents while rock climbing are due to rockfall. In Squamish there are 280 climbing accidents a year.
  
  a)

  What is the expected number of climbing accidents in Squamish due to rockfall?
  
  
  b)

  What is the standard deviation of climbing accidents in Squamish due to rockfall?
  
  
  c)

  If there were 34 accidents in Squamish due to rockfall, would that be usual or unusual?
  
  

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