Mean and standard deviation of binomial distribution

Mean and standard deviation of binomial distribution

Lessons

  • 1.
    P(x)=nCxPx(1p)nxP(x)={_n}C_x \;P^x(1-p)^{n-x}

    nn: number of trials
    xx: number of success in n trials
    pp: probability of success in each trial
    P(x)P(x): probability of getting xx successes (out of nn trials)


    \cdot binomialpdf (n,p,x)(n,p,x)

    \cdot μ=np\mu=np

    \cdot σ2=np(1p)\sigma^2=np(1-p)

    \cdot σ=np(1p)\sigma= \sqrt{np(1-p)}

    Range Rule of Thumb (Usual VS. Unusual):
    \cdot maximum usual value =μ+2σ= \mu+2\sigma
    \cdot minimum usual value =μ2σ= \mu-2\sigma

  • 2.
    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?


  • 3.
    Dealing with a Non-Integer Mean
    How many times would you expect to roll a 6, if you rolled the die 10 times?

  • 4.
    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?