Transcript Chapter 8 Day 3

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Chapter 8 Day 3
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Warm - Up
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Shelly is a telemarketer selling cookies over the phone.
When a customer picks up the phone, she sells cookies 25%
of the time. If 42 people answer the phone today, find the
following:
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What is the probability that Shelly sells cookies to 15 people?
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What is the probability that Shelly sells cookies to at most 8
people?
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What is the probability that Shelly sells cookies to at least 12
people?
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Mean and Standard Deviation
of a Binomial Random Variable
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If a count X has the binomial distribution with number
of observations n and probability of success p, the
mean and standard deviation of X are
  np
  np 1  p 
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Example
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Jack burns 15% of his pizzas. If he cooks 9 pizzas, how
many will he burn on average?
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What is the standard deviation of the number of pizzas
burned?
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What is the probability of exactly 7 pizzas cooked (not
burned)?
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What is the probability that at least 1 of the pizzas is
burned?
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Geometric Distribution
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1. Each observation falls into one of just two categories,
which for convenience we call “success” or “failure”
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2. The probability of a success, call it p, is the same for
each observation.
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3. The observations are all independent.
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4. The variable of interest is the number of trials
required to obtain the first success.
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Calculating Geometric
Probabilities
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If X has a geometric distribution with probability p of
success and (1 – p ) of failure on each observation, the
possible values of X are 1, 2, 3, … If n is any one of these
values, then the probability that the first success occurs
on the nth trial is
P X  n  1 p
n1
p
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Example
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Aaron’s love potion works on 90% of women. What is
the probability that the love potion will fail on the 6th
girl he meets?
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What is a success?
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What is the probability of success?
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Construct a probability distribution table and histogram
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What is the probability that the love potions fails on the 6th
girl?
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Construct a cumulative probability histogram.
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Sum of a Geometric Sequence
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The sum of a geometric sequence is
a
1 r
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Where a is the first term, r is the ratio of one term in the
sequence to the next.
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Back to the example…
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Use the formula for the sum of a geometric sequence to show
that the probabilities in the p.d.f. table of X add up to 1.