Transcript chAPTER four

Normal Approximations to
Binomial Distributions
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For a binomial distribution:
n = the number of independent
trials
p = the probability of success
q = the probability of failure
µ = np
σ = √npq
TWO conditions:
np > 5
and
nq > 5
If conditions are met, then the random
variable x is normally distributed.
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Binomial distributions are DISCRETE,
but the normal distribution is
CONTINUOUS.
The binomial probability formulas from
CH 4 are for exact probabilities. i.e.,
P(X = 4)
To adjust for continuity, move 0.5 units
to the left and right of the midpoint.
This allows you to include all x-values
in the interval. i.e., P(3.5 < X < 4.5)
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1. The probability if getting between 39
and 77 successes, inclusive.
2. The probability of getting at least 80
successes.
3. The probability of getting fewer than
50 successes.
1.
2.
3.
4.
5.
6.
Find n, p, and q
Is np > 5? Is nq > 5?
Find µ and σ
Correct for Continuity (+ 0.5)
Find z
Use standard normal table to finish
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24. A survey of US adults ages 50-64
found that 70% use the Internet. You
randomly select 80 adults ages 50-64 and
ask them if they use the Internet.
A. Find the prob that at least 70 people
say they use the Internet.
B. Find the prob that exactly 50 people
say they use the internet.
C. Find the prob that more than 60
people say they use the internet.
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25. About 34% of workers in the US are
college graduates. You randomly select
50 workers and ask them if they are a
college graduate.
A. Find the prob that exactly 12 workers
are college graduates.
B. Find the prob that more than 23
workers are college graduates.
C. Find the prob that at most 18
workers are college graduates.
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D. A committee is looking for 30
working college graduates to volunteer
at a career fair. The committee
randomly selects 125 workers. What is
the probability that there will not be
enough college graduates?