Binomial Distribution

  • BINP

    • B = Binary process = 2 process

    • I = Independent event

    • N = Number of trials

    • P = Probability of success

  • Binomial Probability

    • binompdf(n, p, x)

    • n=trials

    • p=probability

    • x=value

    s\! SNI r \_ubxd sapt.p s u ueo iXi(x - u) = (x)d

  • Calculator

    • 2ND + VARS (DISTR)

    Tl-B4 Plus Sirver Edtim TEXAS INSTRUMENTS z: normal cdf( 3: i noNarr'lC 4: inoT1. voRMnIn FS

  • A: binompdf / B: binomcdf

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  • binompdf vs binomcdf

    P (X = c) = binompdf(n,p, c) n -\> number of trials p -\> probability of success This finds the probability of exactly c successes, for some number c.

    P (X c) = binomcdf(n, p, c) n -\> number of trials p -\> probability of success This finds the probability of c or fewer successes.

Practice Questions for Binomial Distribution

  • A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 4% are defective. In a quality control procedure, we randomly select 40 toasters for testing.

    • Determine the probability that exactly one of the toasters is defective

    PIX= D

  • Find the probability that at most two of the toasters are defective

    ト 0 っ )e-S い 0 一 ド 3 よ ・ 78

  • Find the probability that more than three toasters are defective

    乙 0 介 个 0 勹 % フ 9

Geometric Distribution

  • BINP

    • Not given the number of trials

  • Question Format

    • How many trials until a success

  • Geometric Probability

    • geometpdf(p,x)

    • geometcdf(p,x)

    • p=probability of success

    • x=number of trials until 1 success

    .13 .16 .14 .12 .10 .08 .06 .02 0.0 3 fail before success 1/6 2nd roll probability is the probability of a failure followed by a success. 2 3 4 567 Number of rolls AP Statistics, Section 9 10 k-l 6

Practice Questions for Geometric Distribution

  • There is a probability of 0.09 that a vaccine will cause a certain side effect. Suppose that a number of patients are inoculated with the vaccine. We are interested in the number of patients vaccinated until the first side effect is observed

    • Find the probability that exactly 4 patients must be vaccinated in order to observe the first side effect.

    ![Т1-84 PIus S'tver Editj(n ф TEns [NSTRUMENTS ](./media/image125.png)

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  • What is the probability that the number of patients vaccinated until the first side effect is observed at most 5?

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Mean and Standard Deviation

Binomial Geometric Mean Variance Standard Deviation Mean Variance Standard Deviation npq npq 1

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